Working Paper Tracking the new economy: Using growth theory to detect changes in trend productivity

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1 econsor Der Open-Access-Publkaonsserver der ZBW Lebnz-Informaonszenrum Wrschaf The Open Access Publcaon erver of he ZBW Lebnz Informaon Cenre for Economcs Kahn James A.; Rch Rober Workng Paper Trackng he new economy: Usng growh heory o deec changes n rend producvy aff Repor Federal Reserve Bank of New York No. 59 Provded n Cooperaon wh: Federal Reserve Bank of New York uggesed Caon: Kahn James A.; Rch Rober 23 : Trackng he new economy: Usng growh heory o deec changes n rend producvy aff Repor Federal Reserve Bank of New York No. 59 Ths Verson s avalable a: hp://hdl.handle.ne/49/6647 Nuzungsbedngungen: De ZBW räum Ihnen als Nuzern/Nuzer das unengellche räumlch unbeschränke und zelch auf de Dauer des chuzrechs beschränke enfache Rech en das ausgewähle Werk m Rahmen der uner hp:// nachzulesenden vollsändgen Nuzungsbedngungen zu vervelfälgen m denen de Nuzern/der Nuzer sch durch de erse Nuzung enversanden erklär. Terms of use: The ZBW grans you he user he non-exclusve rgh o use he seleced work free of charge errorally unresrced and whn he me lm of he erm of he propery rghs accordng o he erms specfed a hp:// By he frs use of he seleced work he user agrees and declares o comply wh hese erms of use. zbw Lebnz-Informaonszenrum Wrschaf Lebnz Informaon Cenre for Economcs

2 Trackng he New Economy: Usng Growh Theory o Deec Changes n Trend Producvy James A. Kahn and Rober Rch Federal Reserve Bank of New York aff Repors no. 59 January 23 JEL classfcaon: O4 O5 C32 Absrac The acceleraon of producvy snce 995 has promped a debae over wheher he economy s underlyng growh rae wll reman hgh. In hs paper we propose a mehodology for esmang rend growh ha draws on growh heory o denfy varables oher han producvy namely consumpon and labor compensaon o help esmae rend producvy growh. We rea ha rend as a common facor wh wo regmes hgh-growh and low-growh. Our analyss pcks up srkng evdence of a swch n he md-99s o a hgher long-erm growh regme as well as a swch n he early 97s n he oher drecon. In addon we fnd ha producvy daa alone provde nsuffcen evdence of regme changes; corroborang evdence from oher daa s crucal n denfyng changes n rend growh. We also argue ha our mehodology would be effecve n deecng changes n rend n real me: In he case of he 99s he mehodology would have deeced he regme swch whn wo years of s acual occurrence accordng o subsequen daa. Research and Marke Analyss Group Federal Reserve Bank of New York New York New York 45 e-mal: [email protected] [email protected]. The auhors hank Chang-Jn Km and Chrsan Murray for asssance wh programs used n performng he compuaons and semnar parcpans a NYU and Carnege-Mellon for her commens. The vews expressed n hs arcle are hose of he auhors and do no necessarly reflec he poson of he Federal Reserve Bank of New York or he Federal Reserve ysem.

3 Dscernng underlyng rends n producvy growh has long been a goal of boh polcymakers and economss. A leas snce olow s 956 poneerng work on long-erm growh economss have undersood ha susaned producvy growh s he only source of long-erm growh n lvng sandards. I s also mporan for shor-erm polcy analyss as any assessmen of oupu gaps or growh speed lms ulmaely derves from some undersandng of wha he rend s. On a quarerly bass however measured producvy growh s exremely volale. Over he poswar perod he average quarerly growh rae of nonfarm producvy has been 2.2 percen annualzed bu he sandard devaon has been 3.9 percen. Moreover he volaly s no confned o hgh frequency flucuaons. Producvy growh s also cyclcal ypcally declnng a he onse of a recesson and rsng durng a recovery. Thus s ofen only years afer he fac ha any change n s long-erm rend wll be apparen. I s wdely beleved ha he dffculy of deecng a change n rend growh conrbued sgnfcanly o he economc nsably of he 97 s as polcymakers were unaware of he slowdown n producvy growh for many years and only much laer were able o dae he slowdown a approxmaely 973. Ths resuled n overesmang poenal GDP a leas so he convenonal wsdom goes and seng neres raes oo low and double-dg nflaon followed no long afer. In recen years aenon has urned once agan o producvy because of speculaon ha s rend growh rae may be pckng up agan. The growh rae of nonfarm oupu per hour ncreased by approxmaely percen begnnng n 996 relave o he perod and by abou.3 percen relave o The acceleraon of producvy pus s growh rae durng hs 5-year perod close o where was durng he mos recen perod of srong growh ee for example ms 2 who wres ha durng he 97 s unemploymen rose and nflaon rose because of real dsurbances ha lowered growh.... nce such sagflaon had no occurred before on such a scale hey faced a dffcul nference problem whch ook hem some years o unravel.

4 2 from roughly 948 o 973. Ths has provoked a debae over wheher we can expec an exended perod of more rapd producvy growh. Rober Gordon 2 for example arbues abou half of he acceleraon o a cyclcal effec and much of he remander o measured producvy growh n he echnology secor. Ohers e.g. roh 22 fnd evdence ha producvy growh has splled over no oher secors hrough capal deepenng. Much of he dffculy n evaluang he argumens n hs debae relaes o he ssue of separang rend from cycle n he daa. For example f Gordon had assumed an acceleraon n rend GDP hen he would have found a smaller or non-exsen oupu gap and consequenly would be less lkely o arbue he producvy acceleraon o cyclcal effecs. Thus whou more nformaon eher sory new economy: accelerang producvy and oupu; or old economy: ncreased producvy growh confned o IT secor all else s cyclcal seems conssen wh he producvy daa. Ths s a problem ha plagues any effor o dsngush rend from cycle n a sngle me seres over a relavely shor perod of me. Moreover even apar from he dffculy of dsngushng rend from cycle s reasonable o queson wheher much of anyhng can be learned from fve or sx years of daa on a seres as volale as producvy growh. In hs paper we aack hs problem by drawng on sandard neoclasscal growh heory o help us denfy varables oher han producvy self namely consumpon and labor compensaon ha should help o esmae he rend n long-erm growh. We rea ha rend as a sochasc process whose mean growh rae has wo regmes hgh and low wh some probably of swchng beween he wo a any pon n me. We model he busness cycle as a second process common o all of he varables n he analyss also wh wo regmes of s own based on he so-called pluckng model of Fredman

5 3 There are several advanages o our approach. Frs we show ha aggregae producvy daa alone do no provde as clear or as mely a sgnal of srucural change as does he on sgnal from he seres we examne. econd we do no have o choose break daes a pror as we le he daa speak for hemselves. Thrd he model no only provdes nformaon abou when regme swches occurred also provdes esmaes of how long he regmes are lkely o las. Ths las propery conrass wh even he mos sophscaed srucural break ess such as hose descrbed by Hansen 2. Also worh emphaszng s ha our use of heory enables us o resrc our analyss o a low dmensonal sysem of varables and o mpose parameer resrcons n he esmaon procedure. Our approach conrass wh aheorecal applcaons of facor models ha nvolve a large number of varables or ha do no place heory-based resrcons on esmaed coeffcens. 2 Here here are boh advanages and dsadvanages: Our model may no provde as gh a f o he daa as would a more eclecc approach bu s lkely o be more robus o srucural changes n he economy. Our analyss pcks up srkng evdence of a swch n he md-99 s o a hgher longerm growh regme as well as a swch n he early 97 s n he oher drecon. Whle hese conclusons may come as no bg surprse our analyss has furher mplcaons. Frs one could no conclude ha here was a swch o a hgher regme on he bass of producvy daa alone or even wh he addon of a varable o conrol for he busness cycle. Only he corroborang evdence from consumpon and labor compensaon can swng he balance n favor of a regme swch. econd he ably o dscern he swch o a hgher-growh regme based on our analyss has appeared relavely recenly. Only wh daa hrough he end of 999 could one conclude ha wh farly hgh probably a swch had occurred. 2 ee for example ock and Wason 989 forhcomng.

6 4 I. Background: The Neoclasscal Growh Model Over fory years ago Ncholas Kaldor 96 esablshed a se of sylzed facs abou economc growh ha have guded emprcal researchers ever snce. Hs facs are: labor and capal s ncome shares are relavely consan; 2 growh raes and real neres raes are relavely consan; 3 he rao of capal o labor grows over me and a roughly he same rae as oupu per hour so ha he capal-oupu rao s roughly consan. To hese facs more recen research has added anoher: ha measures of work effor show no clear endency o grow or shrnk over me on a per capa bass. The mporan mplcaon of hs addonal fac s ha wealh and subsuon effecs roughly offse each oher. Ths means for example ha a permanen change n eher he level or growh rae of labor producvy has no permanen mpac on employmen. Of course closer nspecon suggess ha none of he above sylzed facs s lerally rue. Indeed he premse of much work on U.. producvy s ha producvy growh was sysemacally hgher from han was over he subsequen 2-plus years. Bu hey sll provde a sarng pon for modelng economc growh. Tha sarng pon s generally referred o as he neoclasscal growh model. The lnchpns of hs approach are ypcally a consan reurns-o-scale Cobb-Douglas producon echnology n capal and labor consan elascy-of-subsuon preferences for consumpon and exogenous labor-augmenng echnologcal progress. In our analyss we allow for exogenous changes n preferences beween consumpon and lesure o accoun for any long-erm movemens n work effor as measured by hours ha show up n he daa. pecfcally le C denoe aggregae consumpon Y aggregae oupu N populaon measured n person-hours and growng a rae n K capal E effecve labor per un

7 5 of labor npu and L aggregae labor npu n hours. We also assume ha here s a producon funcon Y K LE and preferences defned n erms of a presen dscouned value of uly U ln C / N v where L / N represens he proporon of avalable hours devoed o work. The erm v herefore represens he uly of lesure where v s a concave funcon and s a ase parameer ha mgh shf over me. We assume ha he economy evolves as f a planner solves he followng problem: max e U C/NL/N d subec o C K F K LE where s a dscoun rae. Le c C/NE y Y/NE and k K/NE. Also le W denoe labor compensaon and w W/NE. If we assume for he momen ha E grows a a consan rae g and ha s consan hen frs-order condons for he above maxmzaon problem are as follows: c k n g k F k / c v F2 k / n g F k where s he shadow value of he resource consran emboded n he frs equaon and he oher varables are as defned n he paper. In a seady sae boh and k wll be consan so he sysem

8 6 c n g k F k / c v F 2 k n g F k can be solved for he seady sae values of c k and for fxed values of g and. Ths mples ha he capal labor rao K/L = Ek/ and he rao of consumpon o hours of work C/L = Ec/ wll boh grow a rae g as wll oupu per hour Y/L = Ey/. Also f we assume ha labor s compensaed accordng o s margnal produc hen labor compensaon per hour W/L wll smply equal Y / L and wll also grow a he same rae. To summarze: Proposon : The per capa quanes C/L K/L W/L and Y/L all grow a rae g n he seady sae. Proof: Ths follows from he consancy of c k and y and her defnons. The precedng resul nealy characerzes he relaonshps beween varables of neres under he assumpon ha g and are consan over me.e. whn a gven regme. Of course hs paper s predcaed on he possbly ha boh and g n parcular may have experenced mporan changes n he poswar perod. To dspense wh he easy case frs level changes n have no mpac on he conclusons of he prevous paragraph. The permanen componens of he capal-labor rao oupu per hour consumpon relave o hours and labor compensaon per hour should all connue o move ogeher excep for ransory varaon n response o changes n labor supply. For example f falls he resul wll be an ncrease n L/N bu K and C wll adus proporonally. o we have Proposon 2: The seady-sae values of c / k / and y / do no depend on

9 7 Proof: The homogeney of F mples ha and 4 can be expressed n erms of c / k / and y /. nce only eners 3 and w/ F2 k s only a funcon of k / and can vary wh o keep v / consan and c can vary wh o keep 2 sasfed. Thus even permanen movemens n are neural wh respec o he rend n he raos descrbed n Proposon. Changes n g however are no neural excep wh regard o work effor. We have Lemma: The seady-sae value of does no depend on g. Proof: Cobb-Douglas echnology mples y k. Then F k / F2 k / and y / F k / k /. I follows from and 4 ha c / y for any value of g. ubsung hs resul and 2 no equaon 3 proves ha s consan. Togeher wh he Proposon 2 he Lemma s parcularly helpful for undersandng he relaonshp beween employmen and long-erm growh: Any mpac n eher drecon s ransory. Trends n employmen are prmarly a funcon of labor supply.e. demographc and ase facors. 3 The praccal mplcaon of hs s ha we can safely derend employmen whou fear of dscardng mporan nformaon abou underlyng rends n per capa growh. The Lemma also leads mmedaely o he followng non-neuraly resul: Proposon 3: The seady-sae values of c / k / y / and w / vary wh g. Proof: Equaon 4 mples mmedaely ha k / depends negavely on g. nce y / s a funcon of k / changes as well. Equaon 3 hen mples ha mus change wh g snce he Lemma shows ha s consan. Equaon 2 hen mples ha Fnally w / s proporonal o y /. c / mus vary wh g.

10 8 The nuon behnd Proposon 3 s sraghforward: hgher growh makes ndvduals feel wealher and herefore ncreases desred consumpon. The neres rae.e. he margnal produc of capal mus hen rse o keep he level of consumpon n lne wh he curren level of echnology. Ths changes he seady sae capal-labor rao and consequenly he seady sae values of all varables ha are lnked o. Faser growh for example rases fuure consumpon relave o curren levels and herefore dscourages savng and capal accumulaon. The resul s ha he capal-labor rao whle ulmaely growng faser as well also experences a downward shf n s level. A corollary of hs effec s ha he oupu-capal rao shfs upward. Ths effec can be seen raher srkngly n Fgure A whch depcs he oupu-capal rao over he perod Ths rao should shf n he same drecon as he underlyng growh rae whch clearly does. Moreover he sze of he shf s roughly wha one would expec from he model usng plausble parameer values. Proposon 3 hus breaks he exac lnk beween he growh rae of E and he growh raes of C/L Y/L K/L and W/L f he growh rae of E experences permanen 4 changes. I does no however mply ha hese four raos do no hemselves have common long-erm componens only ha he common componen s no he same as he common componen of E. In fac he level shfs n oupu per hour labor compensaon per hour and consumpon/hours should all be he same so ha hose hree varables should have he same permanen componen even n he face of regme shfs n growh. Ths resul s summarzed n he followng: Proposon 4: Whle he seady-sae value of k/y depends on g he seady-sae values of c/y and w/y do no. 3 Of course s possble ha growh affecs demographcs and vce-versa. For example susaned hgher growh seems o be relaed o lower ferly raes. Bu such relaonshps are unlkely o be apparen over a few decades.

11 9 Proof: The frs-order condons -4 mply ha c/y = and w/y = On he oher hand k/y =k/ whch s obvously a funcon of he capal-labor rao whch we have seen depends on g. The upsho of hs revew of he neoclasscal growh model s ha oher daa noably labor compensaon per hour and consumpon relave o hours may provde auxlary nformaon abou he rend n oupu per hour. Ths s no o say ha he nformaon s compleely ndependen and ndeed he source of errors n one seres may be presen n he oher seres as well. For example an naccurae prce deflaor could resul n common msmeasuremen across mulple seres. Noneheless he heory suggess ha consderng hese seres ogeher may provde beer nformaon abou underlyng rends han consderaon of any of hem n solaon. II. Economerc pecfcaon Our esmaon sraegy draws upon he regme-swchng dynamc facor model recenly proposed by Km and Murray 22. The essence of our approach s o examne a number of relaed economc me seres and o use her comovemen o denfy wo shared facors: a common permanen componen and a common ransory componen. The common permanen componen relaes o he movemens n he seres assocaed wh her rend growh rae. On he oher hand he common ransory componen relaes o movemens n he seres assocaed wh he busness cycle. These componens provde a bass o dsngush beween long-run and medum-run changes n he seres as well as o gauge her relave mporance over parcular hsorcal epsodes. 4 We use he erm permanen loosely o mean any change ha s suffcenly long-lasng ha he economy moves arbrarly close o a new seady sae.

12 Whle here are oher me seres models ha also ncorporae permanen and ransory componens he Km and Murray 22 model s unque n ha allows for he possbly ha he componens may be subec o changes n regme. Tha s here may be perodc changes n he underlyng process generang he common permanen and common ransory componens. For he purpose of analyzng he rend and cyclcal movemens n producvy he regme-swchng aspec of he model has several aracve feaures. Frs he regme-swchng permanen componen allows us o accoun for susaned changes n rend growh whou makng he growh process self nonsaonary. Consequenly we can no only address he ssue of a pos-973 producvy growh slowdown bu also a pos-995 producvy growh resurgence. econd he regme-swchng common ransory componen allows us o accoun for possble asymmeres across booms and recessons. In parcular we can capure he dea proposed n Fredman s pluckng model model ha economc flucuaons are largely permanen durng expansons and largely ransory durng recessons. Las whle he model allows for perodc changes n he processes generang he common permanen and common ransory componens he mng of he swches does no need o be specfed pror o esmaon. Raher he mng of he swches s deermned as one of he oucomes from he esmaon procedure. Followng Km and Murray 22 we can descrbe he regme-swchng dynamc facor model as follows. 5 uppose we consder a number of me seres ndexed by. Le Q denoe he growh rae of he h ndvdual me seres. I s assumed ha he movemens n each seres are governed by he followng process: Q D x z 5 where D s he average growh rae of he seres denoes he growh rae of a permanen

13 componen ha s common o all seres x denoes he growh rae of a common ransory componen and z denoes an dosyncrac componen. The parameer he permanen facor loadng ndcaes he exen o whch he seres moves wh he common permanen componen. mlarly he parameer ndcaes he exen o whch he seres s affeced by he ransory componen. 6 The common permanen componen s assumed o be subec o he ype of regmeswchng proposed by Hamlon 989 n whch here are perodc shfs n s growh rae:... p p ~ dn 6 f 7 f Pr[ q Pr[ p 8 where s an ndex of he regme for he common permanen componen. The ranson probables p and q ndcae he lkelhood of remanng n he same regme. Under hese assumpons he common permanen componen grows a he rae /... p when = and a he rae /... p when =. The common ransory componen x s also subec o regme-swchng: x * * * 2 x 2 x2... p x p ~ dn 9 f 2 2 f 2 5 Addonal deals are provded n he Appendx. 6 As we demonsrae shorly he formulaons for he common permanen componen and common ransory componen have dfferen mplcaons for her effecs on he ndvdual me seres. pecfcally he level of he common permanen componen can ncrease over me whle he level of he common ransory componen s saonary.

14 2 where Pr[ 2 2 q2 Pr[ 2 2 p2 2 s an ndex of he regme for he common ransory componen wh ranson probables p 2 and q 2. The permanen and ransory regmes are assumed o be ndependen of each oher. The resrcon of un varance for he error erms of he wo processes s an denfyng resrcon snce and x are of ndeermnae scale. The parameer represens he sze of he pluck wh mplyng ha he common ransory componen s plucked down durng a recesson. Fnally he dosyncrac componens are assumed o have he followng srucure: z z 2 2 z 2... p z p ~ dn 2 where all nnovaons n he model are assumed o be muually and serally uncorrelaed a all leads and lags. Whle he wo regmes are no drecly observable s neverheless possble o esmae he parameers of he model and o exrac esmaes of he common componens. 7 An mporan byproduc from he esmaon procedure s ha we can draw nferences abou he lkelhood ha each common componen s n a specfc regme a a parcular dae. The nferences can be based on a real me assessmen whch provdes an esmae of he curren regme as of dae based only on nformaon hrough dae or a rerospecve assessmen ha ncorporaes nformaon for he enre sample. 8 Of course he rerospecve assessmen s a more relable esmae of pas regmes because ncorporaes subsequen daa bu he real-me assessmen s useful as a gauge of wha analyss could realscally have known a he me. 7 Km and Murray 22 dscuss how he regme-swchng dynamc facor model can be cas n a sae-space represenaon and esmaed usng he Kalman fler. More deals of how we appled her mehods o he presen sudy are n he Appendx. 8 The desgnaon real me s poenally msleadng on wo couns. Frs he parameer esmaes are based on he enre sample hough resuls based on rollng parameer esmaes gong back o 997 gave very smlar resuls. econd he daa may have undergone subsequen revsons ha would have been unavalable as of he me of he assessmen.

15 3 Our daa conss of four quarerly seres on labor producvy real compensaon per hour consumpon deflaed by hours of work and hours of work self. All of he daa excep aggregae consumpon refer o he prvae nonfarm secor. The selecon of he seres and her subsequen ransformaon for he esmaon are based on he mplcaons of he growh model n he prevous secon whch provdes gudance on her usefulness for denfcaon of he common permanen and ransory componens. Wh regard o he hours seres as we have seen he growh model mples ha s permanen componen s unrelaed o he permanen componen of he oher hree seres. Raher han esmae a second permanen componen we smply derend hs seres usng he Hodrck-Presco 98 fler and nclude solely o help refne he esmae of he common ransory componen. Wh regard o he dynamc specfcaon of he common and dosyncrac componens our dagnosc checkng procedure suggesed ha he common permanen componen should nclude one lagged value of he common ransory componen should nclude wo lagged values of x and ha he dosyncrac componen should nclude one lagged values of z for each seres. The resuls from econ I Proposon 4 n parcular mply resrcons on he whch represen he permanen facor loadngs n he model. pecfcally we resrced he esmaed permanen facor loadngs for producvy real compensaon per hour and consumpon per hour o be equal. In addon we se he value of he permanen facor loadng for derended hours o be equal o zero. III. Resuls As descrbed above our benchmark model uses he hree varables ha growh heory suggess should have approxmaely he same permanen componens: Real oupu per hour varable real labor compensaon per hour varable 2 and consumpon relave o hours

16 4 varable 3. The ncluson of derended hours varable 4 s desgned o help capure he ransory or busness cycle componen of he daa. As we have seen whle he capal-labor rao should also exhb he same growh as oupu per hour whn a growh regme boh heory and he daa sugges ha can ump subsanally beween regmes so we exclude from our sysem. One fnal specfcaon ssue relaes o he synchronzaon of he daa. The hree rendng varables were seleced prmarly wh a vew o helpng denfy he common permanen componen. They are no necessarly concden ndcaors wh respec o he ransory componen. In heory would be possble o allow for a more general lead/lag srucure n our sysem bu hs would grealy ncrease he number of parameers o esmae. As an alernave we frs examned he cross-correlaons of he four seres. We found ha he frs wo varables producvy and labor compensaon per hour boh ended o lead he oher wo seres by abou hree quarers. To capure hs asynchronzaon n he esmaon we lagged varables and 2 by hree quarers n he sysem descrbed above. 9 A. Parameer Esmaes The frs se of resuls n Table provdes he parameer esmaes for our benchmark model wh hese four varables. As already menoned we resrc he loadng facor on he common permanen componen o be he same for he hree rendng varables a resrcon ha we es and fal o reec for hs specfcaon. The daa cover 947:Q-22:Q2 hough because he frs wo varables are lagged hree quarers her growh raes cover he perod 9 A mnor drawback o hs procedure s ha he las hree observaons of varables and 2 are no used n esmang he parameers of he model. We do ncorporae hem n he perod-by-perod assessmens of he sae varables as descrbed below. Esmaes of he donsyncrac varances are omed from Table for he sake of brevy.

17 5 947:Q2-2:Q3 whle he growh raes of consumpon and derended hours varables cover 948:Q-22:Q2. The resuls ndcae ha he model yelds precse esmaes of mos of he parameers of neres: The loadng facors on boh he permanen and ransory componenshe ranson probables and he shf parameers conneced wh he regmes all come n sgnfcan. The dfference beween he low and hgh permanen regmes works ou o be Ths corresponds o roughly.5 percen on an annualzed bass very close o he dfference beween he and growh raes. The ranson probables for he permanen regmes mply ha he uncondonal probably of beng n he hgh growh regme s.593 whch as we shall see reflecs he nference ha he economy was n he hgh growh regme 59.3 percen of he me beween 947 and he presen. The ransory process s esmaed o be a hump-shaped auoregressve process ypcal of he busness cycle bu wh a sgnfcan negave pluck. The four coeffcens whch represen he loadng facors on he ransory process are all esmaed very precsely and have he expeced sgns. Noe ha he loadng facor for consumpon/hours s negave reflecng he fac ha hours are more cyclcal han consumpon. The posve esmaes for he loadng facors on he real compensaon and producvy varables ndcae ha hose wo varables assocae posvely wh he ransory componen albe leadng by hree quarers relave o he oher wo varables snce hey ener he sysem lagged by hree quarers. B. Growh Regme Assessmens Before furher descrbng he permanen and ransory componens of producvy growh however s nsrucve o examne he nferred probably of beng n he hgh- or lowgrowh sae over me. There are wo ways o examne hs. The frs s n real me : A each

18 6 pon n me usng only daa hrough ha pon n me wha probably would one have assgned o beng n he hgh-growh sae? The second way s rerospecvely: Gven wha we now know has happened hrough 22:Q2 wha can we say lookng back over me abou he lkelhood of beng n he hgh growh sae? Obvously he wo assessmens concde a he end.e. as of 22:Q2. Even whn he real me approach wo praccal ssues arse. Frs here s he maer of daa revsons. The hsorcal seres we have oday have been revsed numerous mes over he years so he daa runcaed a some dae does no correspond o wha anyone would acually have known. We gnore hs problem n he presen sudy bu plan o address n subsequen work. econd s no praccal o have rollng esmaes of parameers especally f regme shfs occur nfrequenly. Over a shorer sample few f any regme swches wll be observed makng mpossble o esmae ranson probables. And oher parameers wll be dffcul o esmae precsely as well. Consequenly n lookng a real me assessmens of he sae vecor we wll rely on parameer esmaes from he full sample. 2 There s also a echncal ssue relaed o he mng of he daa seres. nce Q and Q 2 are lagged by hree perods f we were smply o assess he sae varable gven daa hrough a gven observaon number we would be gnorng he mos recen hree daa pons for hose wo seres. For example a sandard applcaon of he Kalman fler a dae would yeld an assessmen of he sae gven daa hrough perod ˆ E Q Q2 Q3 Q4 ; Q Q2 Q3 Q4 ;.... Hamlon 994 refers o hese wo approaches as usng a zero-lag versus full-sample smooher. 2 We expermened wh rollng parameer esmaes gong back fve years and found ha he resuls were no sgnfcanly dfferen.

19 7 In erms of he acual underlyng daa however would really be provdng E Q ~ 3 Q ~ 2 3 Q ~ 3 Q ~ 4 ; Q ~ 4 Q ~ 2 4 Q ~ 3 Q ~ 4 ;... where he ~ denoes he varable ndexed by s rue me perod. Forunaely s relavely sraghforward o parally updae he sae and regme assessmens. Ths nvolves condonng on hree subsequen observaons of Q and Q 2 a each pon n me o ge ˆ 3 E E Q Q ~ 3 Q ; 2 Q ~ Q ~ Q Q ~ Q Q Q ; Q ~ Q ~ Q ~ Q 3 3 Q ~ Q 4 4. ;... ;.... Here we use +3 o denoe Q and Q 2 observed hrough +3 and Q 3 and Q 4 observed hrough me. Ths smply undoes he saggerng so ha he nformaon se s appropraely algned. Addonal deals on he paral updang procedure are provded n he Appendx. These wo regme assessmens are ploed n Fgure 2. The vercal axs s he probably of beng n he hgh-growh regme. The rerospecve assessmen presens a very clear pcure: The economy was n a hgh-growh sae unl he early 97 s followed by a roughly 2-year low-growh regme followed by a swch back o hgh-growh n he second half of he 99 s. Perhaps he only surprse here s how unambguous he curren assessmen s. The probably ha he economy was n he hgh-growh regme surpassed.95 n 998:Q4 and has no subsequenly fallen below.97. Gven he 3-quarer lead for producvy hs daes he acceleraon of producvy growh a 998:Q. If we use a more lenen.5 hreshold we would dae he acceleraon a 997:Q3. I s worh nong ha he paral updang mehodology descrbed earler can make a subsanal dfference n assessng curren condons. For example whou ha s gnorng he las hree observaons of producvy and real labor compensaon per hour he esmaed

20 8 probably ha he economy s n he hgh-growh regme falls from.9997 n 2:Q4 o.957 n 22:Q2. Addng back he nformaon conaned n hose observaons resuls n a 22:Q2 esmae of.974. As he prevous dscusson makes clear however he rerospecve esmaes do no mean ha as of 997:Q3 we acually could have made such an opmsc assessmen. Wh daa only hrough 998:Q4 he hgh-growh probably assessmen would have been.69 raher han.95. The probably only surpassed.95 when we nclude daa hrough 999:Q4. Thus hndsgh provdes us wh roughly a one-year ump on dang he producvy acceleraon. And s easy o undersand why lookng a Fgure 2. In real me here were a lo of false alarms pos-973 epsodes when appeared ha producvy growh mgh shf no hgh gear. These ended o occur durng recoveres when producvy growh dd n fac ncrease and when was oo soon o ell nowhsandng an effor o dsenangle cycle from rend wheher he hgher growh rae would be susaned. Noneheless even n real me would have been clear from hese echnques wh daa hrough 999:Q when he probably assessmen frs opped.9 ha here had been a change n regme back o sronger producvy growh begnnng n 998:Q2. Whle ceranly he dea of a new economy wh srong producvy growh had ganed many adherens well before 999 here were also pleny of nay-sayers and few of he opmss would have venured o base her vews on obecve sascal analyss. 3 For compleeness we can also look a he assessmen of he ransory regmes and he overall ransory and dosyncrac componens of he seres. The rerospecve probably of 3 Indeed opmsc vews go back as early as 997 see for example The New York Tmes Augus "Measurng Producvy n he 9's: Opmss vs. kepcs" by Lous Uchelle. The opmsm appears however o have been based on somehng oher han he producvy daa hemselves abou whch here was much skepcsm see Corrado and lfman 999. Of course pessmss have also based her vews on skepcsm abou he daa e.g. Roach 998.

21 9 beng n he plucked down sae s ploed n Fgure 3. Here he probably assessmens are a lle more ambguous whch s no surprsng consderng ha he regmes hemselves are relavely ransory. Noneheless he more promnen spkes all concde wh NBER-defned recessons hough several recessons mos noably he 99-9 recesson are mssed enrely and several ohers show up wh a relavely low probably. I s perhaps nsrucve ha he 99-9 recesson does no regser n hs pcure. The dea of a pluck s a sharp downurn followed by an equally sharp recovery suffcen o ge he economy back o rend. The 99-9 recesson was characerzed by a relavely mld downurn followed by an unusually slow and gradual recovery. If we nsead look a he oal common ransory componen whch ncludes an auoregressve process as well as he pluck n Fgure 4 we see ha hs recesson does n fac regser as do all of he poswar recessons albe very mldly. If we examne he permanen and ransory componens of producvy growh drecly Fgure 5 we see ha he permanen componen clearly ndcaes changes n rend n he early 97 s and md-99 s wh lle apparen cyclcal resdue. 4 A he same me however he model sll assgns a lo of varaon o he dosyncrac componen Fgure 4. Presumably hs reflecs he hgh volaly of quarerly producvy growh volaly whch canno be easly be explaned away by cyclcal facors. Whle ncluson of more cyclcal varables mgh reduce he role of he dosyncrac componen somewha we dd no pursue hs as s would be unlkely o aler sgnfcanly he assessmen of permanen regmes ha s our focus. D. The Relave Imporance of Addonal Varables Fnally from a mehodologcal perspecve one may ask how mporan s he use of addonal seres n helpng o denfy changes n rend growh. To answer hs we use he same 4 Ths conrass wh Km and Murray 2 whose esmaed permanen aggregae componen shows subsanal downward movemen durng recessons.

22 2 economerc model bu wh only wo seres nonfarm oupu per hour and derended hours varables and 4 from he prevous analyss. Thus we are lookng o esmae rend growh wh producvy daa alone usng he derended hours seres o conrol for he busness cycle. The resul of hs exercse s he second se of esmaes n Table. Noe frs ha he esmaes of he ranson probables are very smlar o he earler esmaes suggesng ha he fundamenal properes of he regme-swchng dmenson of he model wll be smlar. econdly whle many oher parameers are smlar s clear ha he naure of he permanen componen s very dfferen from he prevous esmae. No only s he facor loadng much hgher.82 o.273 no surprsng snce s he only rendng varable bu s dynamcs are also dfferen as ndcaed by he AR coeffcen of -.96 and nsgnfcan versus -.38 and sgnfcan n he frs se of resuls. These dfferences are refleced n he rerospecve regme assessmens see Fgure 6. Compared o he prevous esmaes he esmaed probably spends a lo more me n gray areas beween ransons and mos mporan ends a around.5 meanng ha he 2-varable sysem sll s undecded abou whch growh regme he economy resdes n oday or over he pas sx years. The dffculy n dsngushng rend from cycle s also manfesed n he volaly of he esmaed permanen componen Fgure 7. Now mos of he movemens n producvy are vewed as permanen because here s lle oher nformaon n he 2-varable sysem o help fler ou he nose. Whle he 2-varable sysem arguably does a beer ob of geng a he ransory componen as he remanng dosyncrac erm s smaller han n he 4-varable sysem from he pon of vew of denfyng changes n underlyng rends he smpler approach appears o fall shor. On he oher hand a look a he real-me probably assessmens n Fgure 6 shows n comparson o Fgure 2 ha he probably assessmens exhb fewer false alarms epsodes

23 2 where he probably ha a regme shf has occurred umps up only o quckly reverse self as more daa come n. For example n 977 he probably of a regme shf back o hgher producvy growh reached.72; n 986 and 992 came o.82 and.67. In all hree nsances hese assessmens proved false n he sense ha he rerospecve probables were subsanally smaller:..8 and.5 respecvely. Perhaps he four-varable sysem s overfng he daa.e. does beer han he wo-varable sysem n avodng ype 2 errors he error of falng o deec a regme change bu makes more ype errors deecng a regme change ha n fac never ook place. To address hs queson we use he wo models o forecas producvy growh a oneand four-quarer horzons. The dea here s ha f he four-varable sysem were overfng he daa he roo mean square error of s forecass would be larger han ha of he wo-varable sysem. We consruced forecass begnnng n 972:Q usng he formulas oulned n Hamlon 994. Consequenly he sample for he one-quarer forecas horzon covers he perod 97:Q2-22:Q2 whle he sample for he four-quarer forecas horzon covers he perod 972:Q- 22:Q2. Table 2 provdes he resuls of hs exercse. For boh forecas horzons he roo mean square error of he wo-varable sysem s larger suggesng ha he four-varable sysem s dong a beer ob nowhsandng he fac ha s prmary nenon s no shor-erm forecasng. Table 2 also provdes he model s forecass of producvy growh for 22:Q3-23:Q2. The four-varable sysem predcs subsanally sronger producvy growh for all four quarers prmarly because of s assessmen of a relavely hgh probably of beng n a hgh-growh regme. Even four quarers ou he model forecass growh subsanally above he sample mean of 2.6 percen nowhsandng ha s bul-n albe slow mean reverson. In fac us he possbly of a swch back o a lower-growh regme bulds n approxmaely a.8 percen per

24 22 quarer declne n growh. Thus condonal on no regme change he forecased growh raes would be abou and 3. percen for he four quarers. The long-run growh rae condonal on remanng n he hgh-growh regme s roughly 2.9 percen. Of course producvy growh s a very nosy seres so a forecas for any gven quarer canno be made wh much confdence. Bu he dfference beween he wo ses of forecass largely reflecs dfferen assessmens of underlyng rends and provdes some dea of he poenal usefulness of he approach adoped n hs paper. 5 Can we say anyhng abou whch of he addonal varables consumpon/hours or labor compensaon per hour s more mporan n helpng o pck up he regme changes? To answer hs queson we esmaed wo addonal specfcaons addng back alernaely one varable or he oher o he 2-equaon sysem. The resuls are llusraed n Fgure 8 n whch all four specfcaons rerospecve regme assessmens are ploed agans each oher. I urns ou ha here s a bg mpac from addng eher varable o he sysem wh he labor compensaon varable appearng o ouperform consumpon/hours n erms of approachng he 4-equaon resuls. The change n gong from hree o four equaons s relavely modes especally f he fourh varable s consumpon/hours. Noe however ha n he more recen daa s consumpon/hours varable ha s gvng he sronger ndcaon ha he economy s n he hghgrowh regme and comes closes o machng he assessmen based on all four seres. E. Changng Volaly Anoher fac ha emerges from our analyss s a dsnc declne n he volaly of producvy growh over me parcularly snce he early 98 s. Ths parallels he fndngs of McConnell and Perez-Quros 2 who documen a break n he volaly of GDP growh a 5 The acual number for 22:Q3 released afer all of hs analyss was done urned ou n fac o be 5. percen n he repor released on December 4 22; see hp://

25 23 around 984:Q. In fac whle he overall uncondonal sandard devaon of producvy growh s 3.6 percen relave o a mean of 2.6 beween 948:Q and 973:Q4 s 4.9 percen. From 974:Q o 995:Q4 falls o 2.99 percen and snce 996:Q s 2.53 percen. The naural place o look for declnng volaly n our framework s n he dosyncrac componens z or he resduals = 4. We compued -year cenered rollng varances of each of he esmaed resduals coverng he perod 958:Q2 o 997:Q2 usng daa from 953:Q2-22:Q2. 6 The resuls shown n Fgure 9 show a srkng declne n only he volaly of he producvy resdual wh no clear paern for he oher seres. One reason hs fndng s of neres s ha f ndeed producvy growh s less nosy han once was movemens n he seres may be more nformave han hey used o be abou changes n he underlyng rend. We esmaed a model allowng for declnng volaly of and found ha he lower volaly dd n fac lead o earler nferences regardng he regme change bu only by abou one quarer. I also resuled n an even hgher assessmen of he probably of beng n he hgh-growh regme durng 22. We do no repor hese resuls n deal as hey do no change he overall pcure bu allowng for heeroscedascy could prove o be mporan for some applcaons such as forecasng. V. Conclusons The vew ha hgher producvy growh s lkely o be susaned has only really ganed somehng approachng a consensus wh he recen recesson. Pror o 2 one could more easly argue ha he ncreased growh raes experenced snce 995 were merely cyclcal or oherwse ephemeral. Tha lack of agreemen no only reflecs he dffculy of separang a me seres no s rend and cycle bu also he sensvy of he resuls o varous assumpons used

26 24 n he decomposon. In he case of producvy he problemac naure of he decomposon s only lkely o be exacerbaed by he nheren volaly of he seres. Polcymakers faced he same dffculy albe n he oppose drecon n he md-97 s when he dramac slowng of producvy growh concded wh a severe recesson. We explore he ssue of he long-erm rend n producvy by adopng a modelng sraegy ha negraes boh heorecal consderaons and recenly developed sascal mehods. In conras o prevous unvarae analyses we underake a mulvarae analyss n whch we explo nformaon from addonal varables ha should be helpful n he denfcaon of he rend and cycle n producvy. pecfcally we exend he daa se o nclude consumpon and labor compensaon as well as derended hours. For our emprcal framework we adop he regme-swchng dynamc facor model recenly proposed by Km and Murray 22. Ths approach has a number of aracve feaures. Frs allows for he esmaon of a common permanen componen and a common ransory componen conssen wh our neres n he rend and cycle n he producvy daa. econd he model allows for rch dynamcs and can accoun for perodc changes n he underlyng processes generang he common componens. Ths laer consderaon s no only mporan for provdng a beer characerzaon of he daa bu s cenral o any dscusson abou a possble shf o he secular growh rae of producvy. Las he naure and mng of he regme changes s deermned as an oucome of he esmaon procedure raher han mposed a pror. In fac one could vew he mpled regme changes and her reasonableness as an addonal merc by whch o udge he adequacy of our approach. 6 We begn n 953 so as o leave ou he Korean War years durng whch here was a bref epsode of unusual volaly.

27 25 We fnd srong suppor n he daa for he noon ha he economy and producvy growh n parcular swched from a relavely low-growh o a hgh-growh regme n he md- 99 s. The annualzed dfference beween he mean growh raes n he wo regmes s esmaed o be approxmaely.5 percen. We also show ha hese echnques could have provded conclusve sgnals of he regme shf by he begnnng of 999. Fnally from a mehodologcal sandpon we argue ha he ncorporaon of addonal nformaon from oher me seres s crucal o he srengh of our conclusons.

28 26 References Corrado Carol and Lawrence lfman Decomposon of Producvy and Un Coss. Amercan Economc Revew Papers and Proceedngs 89 May Fredman Mlon. Moneary udes of he Naonal Bureau. The Naonal Bureau Eners Is 45 h Year 44 h Annual Repor 964 pp.7-25; reprned n The Opmum Quany of Money and Oher Essays by Mlon Fredman ch. 2 pp Chcago: Aldne The Pluckng Model of Busness Flucuaons Revsed. Economc Inqury Aprl Gordon Rober Does he New Economy Measure up o he Grea Invenons of he Pas? Journal of Economc Perspecves Vol.4 No.4 Fall 2 pp Hamlon James D. A New Approach o he Economc Analyss of Nonsaonary Tme eres and he Busness Cycle. Economerca Tme eres Economercs. Prnceon: Prnceon Unversy Press 994. Hansen Bruce E. The New Economercs of rucural Change: Dang Breaks n U.. Labor Producvy. Journal of Economc Perspecves 5 Fall Hodrck Rober and Edward Presco. Pos-War U.. Busness Cycles: An Emprcal Invesgaon." Carnege-Mellon Unversy workng paper 98. Kaldor Ncholas Capal Accumulaon and Economc Growh n F. Luz and D.C. Hague eds. The Theory of Capal New York:. Marn s Press pp Km Chang-Jn and Chrsan Murray. Permanen and Transory Componens of Recessons. Emprcal Economcs forhcomng. Km Chang-Jn and Charles R. Nelson. Fredman s Pluckng Model of Busness Flucuaons: Tess and Esmaes of Permanen and Transory Componens. Journal of Money Cred and Bankng 3:Par McConnell Margare and Gabrel Perez-Quros. "Oupu Flucuaons n he Uned aes: Wha has Changed nce he Early 98s?" Amercan Economc Revew December 2 pp Roach ephen. No Producvy Boom for Workers. Issues n cence and Technology ummer 998.

29 27 ms Chrsopher A. Commen on Evolvng Pos-World War II U.. Inflaon Dynamcs n NBER Macroeconomcs Annual 2 Ben. Bernanke and Kenneh Rogoff eds. Cambrdge: MIT Press. roh Kevn "Informaon Technology and he U.. Producvy Revval: Wha Do he Indusry Daa ay?" Amercan Economc Revew December 22 pp ock James H. and Mark W. Wason. "New Indexes of Concden and Leadng Economc Indcaors." NBER Macroeconomcs Annual "Macroeconomc Forecasng Usng Dffuson Indexes" Journal of Busness and Economc ascs forhcomng.

30 28 Appendx A. ae pace Model We employ he followng sae-space represenaon for our model: Measuremen Equaon: H Q ' Q... Q Q 4 Transon Equaon: V F wh EV V ' and where afer we resrc 3 2 and se H z z z z x x V * 2 * F

31 29 We nex provde a bref overvew of a fler developed by Km 994 ha can be used for approxmae maxmum lkelhood esmaon of he sae-space model wh Markov swchng. We focus our aenon on he ssue of drawng nferences abou he unobserved regmes. For furher deals neresed readers are referred o Km and Murray 22. varables To faclae he dscusson we wll represen he wo unobserved Markov-swchng and 2 by a sngle Markov-swchng varable defned such ha: wh and f and f and 3 f and 4 f and Pr[ 4 p p Condonal on and he Kalman fler equaons are gven by: f P P FP Q H ' HP I P F H ' P F' Q H '[ f H '[ f V HP where and are respecvely an nference on based on nformaon hrough me perod and - gven and ; P and P are respecvely he mean squared error marx of and gven and ; s he condonal forecas error of Q based on nformaon hrough me perod - gven and ; and f s he condonal varance of he forecas error. To keep he Kalman fler from becomng compuaonally nfeasble he followng approxmaons are nroduced o collapse he poserors erms and P no he poseror erms and P :

32 3 Pr[ Pr[ 4 and P = Pr[ '} { Pr[ P The approxmaons resul from he fac ha does no calculae [ E and P does no calculae ' [ E exacly. Ths s because condonal on and s a mxure of normals for > 2. To oban he probably erms necessary o consruc he approxmaons he followng hree-sep procedure s employed. ep : A he begnnng of he h eraon gven Pr[ we can calculae: Pr[ Pr[ Pr[ where Pr[ s a ranson probably. ep 2: We can hen consder he on densy of Q and : Pr[ Q f Q f and hen oban he margnal densy of Q as: 4 4 Q f Q f Pr[ 4 4 Q f where he condonal densy Q f s obaned usng he predcon error decomposon: } ' exp{ T f f Q f A byproduc of hs sep s ha we can oban he log lkelhood funcon: ln T Q f L ln

33 3 whch can be maxmzed wh respec o he parameers of he model. ep 3: We can hen updae he probably erms afer observng Q and he end of perod : Pr[ Pr[ Q Q f Q f Pr[ Q f Q f wh Pr[ Pr[ 4 The las erm provdes he real-me nference abou he unobserved regmes condonal on only conemporaneously avalable nformaon. We can also derve smoohed values of and usng all avalable nformaon hrough perod T. Tha s we can consruc T as well as Pr[ T whch represen he rerospecve assessmens of he sae vecor and unobserved regmes. Because he nferences abou he unobserved regmes do no depend on he sae vecor we can frs calculae smoohed probables. The smoohed probables can hen be used o generae he smoohed esmaes of he sae vecor. The smoohng algorhm for he probables wll nvolve he applcaon of approxmaons smlar o hose nroduced n he basc flerng. The procedure can be undersood by consderng he followng dervaon of he on probably ha k and condonal on full nformaon: Pr[ Pr[ Pr[ T T T k k k Pr[ Pr[ T k k Pr[ Pr[ Pr[ T k k k Pr[ Pr[ Pr[ Pr[ T k k k and

34 32 Pr[ Pr[ T 4 k T The acual consrucon of he smoohed probables requres runnng hrough he basc fler and hen sorng he sequences P P Pr[ and Pr[. For = T - T he above formulas defne a backwards recurson ha can be used o derve he full-sample smoohed probables. I should be noed ha he sarng value for he smoohng algorhm s Pr[ whch s gven by he fnal eraon of he basc fler. T A2. Paral Updang uppose ha addonal observaons become avalable bu only for some subse of he four daa seres represened by Q. pecfcally suppose ha for he subse Q daa are avalable for perods hrough T+3 whereas for Q 2 observaons are only avalable hrough T. Le T 2 denoe he augmened nformaon avalable hrough T.e. ncludng Q T bu no Q T. Through T he sandard Kalman updang algorhm apples gnorng he regme-relaed erm for brevy s sake.e. ˆ Fˆ F[ P FP P Q H' ˆ - P H H' P H H' P for T. To updae furher we smply recognze ha H H - H' P F' Q H ' 2 where H s he approprae submarx of H. We hen erae begnnng a T+ accordng o ˆ T T ' P T T ' ˆ P TT T T P P TT T T H H ' P T T H H ' P T T H H - - Q T H ' P H ' ˆ T T T T and hen ˆ T 2T ' F ˆ T 2T ' T T ' P FP T T ' F' The eraon can hen proceed forward f subsequen observaons on Q become avalable. In our case we essenally have hree addonal observaons on wo of he varables snce hey appear lagged by hree quarers. To ake hem no accoun a any pon n me we can compue ˆ 3' ha s he assessmen of he sae vecor gven he hree addonal observaons of he wo seres ha would oherwse be gnored because hey are lagged by hree.

35 33 quarers. To oban ˆ 3' we erae forward o ge ˆ 3 3' and P 3 3' and hen eravely smooh backwards usng e.g. - ˆ ˆ P H H ' P H ˆ ˆ. 2 3' 2 2' 2 2' 3 2' 3 3' 3 2' The resul s an mproved esmae of he sae vecor one ha ncorporaes he mos recen values of all of he varables.

36 34 Table : Esmaon of Model Coeffcen 4 equaon sysem p q p q * * equaon sysem logl Noe: The esmaon also produces esmaes of he varances of he dosyncrac errors no repored here.

37 35 Table 2: Forecas Performance 2-varable sysem 4-varable sysem Roo Mean quare Errors -quarer horzon year horzon Forecas quarer ahead 22:Q3 3.4% 4.3% 22:Q :Q :Q Noe: All fgures are a annualzed percenage raes. The average annualzed growh rae of producvy log dfferences over he full sample s 2.6 percen wh a sandard devaon of 3.6.

38 Fgure : Evdence on he Level hf of he Capal-Labor Rao Y/C Y/W Y/K Log cale 972:=

39 Fgure 2: Assessmen of Growh Regmes Rerospecve Real Tme 37 ProbHgh-Growh

40 . Fgure 3: Probably of a Negave Pluck hadng= NBER recesson ProbLow Transory Regme 38

41 4 Fgure 4: Transory and Idosyncrac Componens of Producvy hadng= NBER recesson Idosyncrac Componen Transory Componen 39 Pc. Devaon from Trend

42 5 Fgure 5: Trend Producvy Producvy Permanen Componen 4 log scale x Noe: Ths s a plo of +3 agans he logarhm of producvy growh a dae.

43 Fgure 6: Regme Assessmen whou Oher Trendng Varables Rerospecve Real Tme 4 ProbHgh-Growh

44 5 Fgure 7: Producvy and s Permanen Componen Two-eres ysem Producvy Permanen Componen 42 log scale hadng= NBER recesson

45 Fgure 8: Relave Imporance of Varables for Regme Assessmen Equaon ysem Excludng W/L Excludng C/L 2-Equaon ysem 43 ProbHgh-Growh

46 Fgure 9: Varance of Idosyncrac Resduals -year Rollng Esmaes Y/L W/L C/L L 44