Real-Time Forecasting Revisited: Letting the Data Decide

Transcription

1 Real-Tme Forecasng Revsed: Leng he Daa Decde Jackson Kchen John Kchen Revsed Sepember 2012 Orgnal verson June 2012 Paper prepared for he Naonal Assocaon for Busness Economcs 2012 Menns Award for presenaon a he NABE 2012 Annual Meeng. Vews epressed n he paper are he auhors and do no represen he vews of he U.S. Deparmen of he Treasury or any oher nsuon. Correspondence: John Kchen john.kchen@reasury.gov (202)

2 Absrac Real-me GDP forecasng also ofen known as nowcasng produces esmaes for curren-quarer real GDP growh ypcally based on a cenered value from a se of esmaes from ncomng ndcaors. These real-me measures are usually nended o be daa-based and o no be based on forecaser judgmen or add facors. Even so esmaon mehodologes n hs research area -- and pror versons of he sysem we use -- ypcally have been consraned by usng varous fed relaonshps; for eample a fed hsorcal sample horzon and fed emprcal specfcaons for he ndcaor varables. Ths paper descrbes he mehodology esmaon and sofware code for a more fleble real-me GDP sysem we have developed ha allows he daa o decde he bes real-me GDP forecas for varyng sample horzons and varyng specfcaons by ndcaor hrough me. Our sysem uses daa on key ndcaors as hey become avalable (accounng for he jagged-edge naure of he daa n he curren quarer) o generae an esmae of curren-quarer real GDP growh wh weghs for combnng he ndcaor-specfc esmaes deermned by he srengh of he ndcaors hsorcal relaonshps o GDP growh. The mproved sysem searches across a varey of specfcaons and across sample horzons for he ndcaor-specfc esmaons -- choosng he bes specfcaon usng a mnmum Schwarz creron es whle also searchng for he bes sample horzon for mnmzng he mean absolue error for a recen predcon perod. We llusrae he operaon of he sysem for real-me esmaes of real GDP growh over a specfc quarer and eamne he properes of he esmaes and he mplcaons for predcons. We also dscuss poenal addonal applcaons and demonsrae a specfc applcaon for real-me predcons of he monhly change n payroll jobs.

3 Real-Tme Forecasng Revsed: Leng he Daa Decde 1. Inroducon The decsons of busness planners and polcymakers ofen hnge on he curren performance and fuure oulook for he economy. Prvae and publc forecasers herefore have grea neres n esmang and forecasng key economc varables wh a parcular focus on aggregae economc acvy as measured by real GDP growh. The breadh of prvae secor nvolvemen n economc forecasng n he Uned Saes s llusraed by he well-known Blue Chp Economc Indcaors publcaon ha presens he economc forecass for 55 prvae-secor forecasers; publc polcy forecass of he Offce of Managemen and Budge he Congressonal Budge Offce and of he Federal Reserve underpn he fscal and moneary polcy oulooks. Mos shor-run forecass (one o wo years) and nermedae- o longer-range projecons (fve o en years and beyond) are model-based forecass and hey jump off from hsorcal daa and curren quarer values. The conemporaneous curren-quarer performance of he economy s of parcular mporance for curren polcy purposes and also as he base for he fuure projecons. Varous alernave approaches es for makng curren-quarer esmaes for real GDP growh ncludng: behavoral equaon and model-based forecass wh judgmenal add facors; specfccomponen accounng also known as bean counng and llusraed by he Bureau of Economc Analyss (BEA) Key source daa and assumpons supplemenal esmaes; and ndcaorbased esmaes ncludng hose based on concden acvy ndees and more recenly realme or nowcasng daa-based esmaon approaches. Real-me forecass produce esmaes for curren-quarer real GDP growh ypcally based on a cenered value from a se of esmaes from ncomng ndcaors; hey are usually nended o be daa-based and o no nclude forecaser judgmen or add facors. Ths paper presens a new esmang sysem we have developed for makng real-me GDP forecass -- descrbng he mehodology esmaon process and sofware code for a more fleble real-me esmaon sysem ha beer allows he daa o decde he bes real-me GDP forecas for varyng sample horzons and varyng specfcaons by ndcaor hrough me. Esmaon mehodologes n hs research area -- and pror versons of he sysem we use -- ypcally have been consraned by usng varous e ane or predeermned fed relaonshps; for eample a fed hsorcal sample horzon and fed emprcal specfcaons for he ndcaor varables. As n earler real-me esmang analyses our sysem uses he daa on key ndcaors as hey become avalable (and n uneven mng durng he quarer) o generae an esmae of 1

4 curren-quarer real GDP growh based on he esmaed hsorcal ndcaor-gdp relaonshps as well as for he proper daa-avalably pon durng he quarer; he weghs we use for combnng he ndcaor esmaes are deermned by he fs of he hsorcal relaonshps. An mporan new approach n he sysem we presen s ha he mproved sysem now searches across a varey of specfcaons and across sample horzons -- choosng he bes specfcaon by ndcaor for a gven sample usng a mnmum Schwarz creron whle also searchng for he bes sample horzon for mnmzng he mean absolue error for a recen predcon perod. Hence he sysem s now much more fleble n deermnng he specfcaons and sample perods for he ndcaorspecfc esmang equaons boh whn a gven quarer for varyng daa avalably and across quarers hrough me as he sysem s used n ongong real-me esmang effors. And whle research n he area of real-me forecasng and nowcasng has been conduced a varyng levels of heorecal and mahemacal rgor and sophscaon -- and n many cases wh a focus on academc audences -- we beleve our approach s one ha can be readly undersood and useful for he appled and ongong analyses ha are ypcal for mos busness (and publc secor) economss and forecasers. The nen of he paper s o presen nformaon and o be organzed n a manner such ha neresed forecasers and researchers can gan useful nformaon on how he sysem works and beer undersand how can be used n pracce. Followng hs nroducon he second secon of he paper addresses real-me esmaon mehodology and some oher leraure n hs research area. The hrd secon descrbes he modelng and esmaon process for he sysem and dscusses some of he EVews sofware code used o mplemen he sysem. Secon four presens llusrave resuls for he applcaon of he sysem for a specfc recen quarer and he evoluon of real-me GDP esmaes durng ha quarer. Secon fve eamnes he predcon properes for he sysem esmae and for he ndvdual ndcaor-specfc forecass. Secon s dscusses oher poenal applcaons for our real-me esmaon sysem wh a specfc applcaon o show how he sysem can be used n an analogous approach for real-me predcons of he monhly change n payroll jobs. Secon seven furher consders wha useful nformaon can be gleaned from hese ypes of esmaes. Secon egh presens concludng observaons. 2

5 2. General Mehodology and Oher Research and Leraure The research and leraure for real me forecasng and nowcasng have been epandng rapdly over he pas decade. 1 Sock and Wason [2006] surveyed he heorecal and emprcal research on mehods for forecasng economc me seres varables wh many predcors descrbng how ha provdes he opporuny o eplo a much rcher base of nformaon han s convenonally used for me seres forecasng. Kchen and Monaco [2003] descrbed an early verson of a real-me forecasng sysem adoped a he U.S. Treasury o use he broad varey of ncomng daa o consruc real-me esmaes of quarerly real GDP growh. Evans [2005] used a comprehensve analyss o calculae daly real-me esmaes by modelng he growh n GDP as he quarerly aggregae of an unobserved daly process for real economy-wde acvy wh model parameers... esmaed by (quas) mamum lkelhood usng he Kalman fler algorhm. Gannone Rechln and Small [2008] presened an esmang mehodology for producng curren-quarer forecass by adapng a common facors model combnng he dea of brdgng monhly nformaon wh he nowcas of quarerly GDP wh he dea of usng a large number of daa releases whn a sngle sascal framework. In parcular hey clearly addressed he challenge from he evolvng naure of he ncomng daa of he curren quarer: In real me some daa seres have observaons hrough he curren perod whereas for ohers he mos recen observaons may be avalable only for a monh or quarer earler. Consequenly he underlyng daa ses are unbalanced. Appropraely dealng wh hs jagged edge feaure of he daa s key for producng a nowcas ha by eplong nformaon n he mos recen releases has a chance o compee wh judgmenal forecass. [Gannone Rechln and Small 2008 p. 666] 2 Ther approach allows for he nowcas o be condoned on a large number of varables. A varey of sudes have eamned real-me forecasng for Euro area GDP and acvy [Angeln e. al. 2011; Bullgan Golnell and Parg 2010; Drechsel and Maurn 2011; Gannone Rechln and Smonell 2009; Runsler e al 2009]. 3 1 Real-me research and analyses can have wo dfferen defnons: one defnon concerns eamnng he role of he e pos use of he conemporaneously-avalable vnage of daa durng hsorcal perods relave o he curren vnage of daa; he second defnon s he one used n hs paper he use of currenly avalable daa n real me o produce esmaes of he varable of neres as s beng formed and pror o he release of he formal esmae. 2 Ferrara Guégan and Rakoomarolahy [2009] refer o ragged edge daa; boh jagged and ragged refer o he same phenomenon. We use jagged n or dscusson. 3 Prvae frms have also produced propreary and clen-resrced esmaors for curren real GDP growh ncludng Goldman Sachs curren acvy nde and Moody s Analycs hgh frequency model. 3

6 The sysem ha we presen and use for he analyss of hs paper s a descenden of he earler model sysem descrbed n Kchen and Monaco [2003]. The Kchen and Monaco sysem esmaed he ndcaor-specfc hsorcal relaonshps beween monhly ndcaors and real GDP growh (whle properly accounng for ndcaors nra-quarer daa avalably) produced curren-quarer ndcaor-specfc forecass from he esmaed relaonshps and hen combned he ndvdual ndcaor forecass by weghng accordng o he srengh of he ndcaors hsorcal relaonshps o real GDP growh. The sofware code for he sysem we use whle mananng much of he general mehodology was a complee rewrng relave o he pror sysem n order o ncorporae more esmaon flebly and an nheren decson process whn he sysem for choosng he bes esmaons by specfcaons and sample horzons. The pror mehodology was prmarly a consraned esmaon sysem ha ran he varous esmang equaons for largely e ane user-specfed and predeermned specfcaons and sample perods and hen generaed he sysem esmae from hose esmaons. The curren sysem we are now usng s more of an esmaon and decson sysem n ha eravely runs hrough varous alernave specfcaons and samples for he esmang equaons and whn ha process makes he decsons for he bes specfcaons and samples o use n he fnal esmaon. 4 The choces n he sysem are based on he mnmum Schwarz creron o deermne he bes specfcaon for a gven sample sze and usng he mnmum absolue error for he predcon for real GDP growh for a recen perod of me o deermne he bes sample (and for he gven bes specfcaon for ha sample). Hence hs approach s much more n he spr of leng he daa decde allowng for he esmaon process o be deermned n an ongong and evolvng real-me analyss and largely ndependen of subjecve e ane user-specfed relaonshps. A sgnfcan par of he sofware code needed o mplemen boh he pror sysem and he curren sysem nvolves addressng he jagged edge problem of he avalably of daa n he curren quarer and assurng he proper esmaon gven ha problem. The mehodology and sysem operaon are descrbed n more deal below. 3. Modelng Esmaon and Sofware Code Specfcs Ths secon of he paper provdes a descrpon of he operaon of he sysem we use and how s mplemened hrough sofware code. Our real-me forecasng sysem s wren n EVews sofware code -- n 612 lnes of code; 653 lnes f commens are ncluded. We are 4 In an neresng applcaon ha was observed as hs paper was beng wren Wagner Mchalewcz Khouja and McGregor [2004] llusraed a dynamc forecasng genec program modelng approach for forecasng GDP n a nonsac envronmen. 4

7 currenly runnng he sysem n EVews 7.1. The followng dscusson of hs secon descrbes how he sysem: (1) reads n he daa and generaes quarerly-based varables from he monhly daa se specfcally accounng for he dfferen numbers of monhs of daa avalable by ndcaor durng he quarer; (2) esmaes alernave emprcal specfcaons for he ndcaor-real GDP growh relaonshps and searches across hose specfcaons for he bes specfcaon by ndcaor for a gven sample sze accordng o he Schwarz creron sasc (and whle properly accounng for he gven amoun of daa avalable durng he quarer ha s one wo or hree monhs of daa); (3) eraes hrough rollng sample szes for up o 101 pror quarers of hsory and chooses he preferred specfcaon-sample equaon based on he mnmum mean absolue error for predced GDP growh for an egh-quarer perod pror o he curren quarer; (4) generaes a cenered value real-me esmaor from he collecon of ndcaor-based esmaes accordng o relave weghngs based on he R-squared values of he ndcaor esmaed equaons; (5) wres he oupu able for he real GDP growh predcon by ndcaor along wh he specfcaon and sample sze used by ndcaor. The Daa and Dfferng Frequences We use daa on major macroeconomc and fnancal daa seres as key ndcaors from whch o consruc he esmaes of curren-quarer real GDP growh. Mos daa seres are of monhly frequency -- for eample daa on payroll jobs he unemploymen rae ndusral producon real sales orders and shpmens and ohers. Oher daa seres are weekly (unemploymen nsurance clams) or even daly or connuous (sock marke ndees). The sysem as currenly mananed uses daa on 24 ndcaors generally well-recognzed seres (and ha are presened n deal n ables for eamples dscussed below). We manan a daa base of monhly frequency updang he daa seres on an ongong bass as new daa become avalable -- reflecng he jagged edge of he curren perod daa as 5

8 descrbed above. For he hgher frequency seres such as unemploymen nsurance clams and he sock marke ndees we updae he monhly average values for avalable daa and use a random walk assumpon ha any no-ye-observed values for a gven monh are equal o he las observed value. Tha allows us o use a varable wh nal observaons early n a monh o provde nformaon for he begnnng of ha perod. A second daa base ransforms he monhly me-seres vecors of he frs daa base no quarerly daa seres wh monhly elemens (Fgure 1). For eample n he second daa base hree separae payroll jobs seres es for a gven quarer: for he frs monh of he quarer; he second monh of he quarer; and for he hrd monh of he quarer. Tha quarerly daa base allows for an easer way for readng he daa no he EVews compuer program and for managng and ransformng he daa once s n he program. Ths approach assures he proper accounng for he avalably of daa by seres (he proper par of he jagged edge) -- and correc esmaon over me for ha gven real-me avalably -- ye whn a quarerly frequency ha algns wh he dependen varable of neres real GDP growh. Alhough he sysem has he monhly and quarerly frequency aspecs could poenally be run a any me -- even on a daly or nradaly bass -- o updae esmaes as new daa arrve. The EVews program begns by creang a workfle and hen readng n he (quarerly frequency) daa from he second daa base descrbed above. Inal ransformaons of varables are hen made hrough GENR saemens for eample ransformng nomnal seres o real seres and creang he proper quarerly average seres for he cases of varyng daa avalably for dfferng monhly sages of he quarer. Choosng from Alernave Specfcaons The esmaons whn he modelng framework denfy he relaonshp beween a specfc ndcaor varable and real GDP growh durng he curren quarer. The specfcaons herefore use he dependen varable of y = real GDP percenage change durng he quarer a an annual rae and rgh-hand-sde varables as varous ransformed forms of = level of he h ndcaor varable. The EVews compuer code uses sequenal FOR-NEXT loops o run hrough he alernave specfcaons by ndcaor varable (and separae ses of he saemens by he sage of he daa avalably of he jagged edge for he quarer) and ess for he bes specfcaon for a gven sample sze by comparng Schwarz creron sascs. The 6

9 7 specfcaons currenly consdered n he program (and by numercal value denong he specfcaon n he oupu) are 5 : 1. Frs dfference specfcaon: e y ) ( 1 2. Frs and lagged dfferences specfcaon: e y ) ( ) ( Percenage change specfcaon: e y Lagged percenage change specfcaon: e y Curren level and frs dfference: e y ) ( Curren and lagged percenage changes specfcaon: e y Alhough he above specfcaons ha we have ncluded n he sysem code provde a relavely good range of alernaves he sysem obvously could consder an even greaer number and range of alernave specfcaons and hereby poenally make he sysem even more encompassng n erms of leng he daa decde. 6 Noneheless we are comforable ha he range of specfcaons we have ncluded for he analyss and presenaon n hs paper provdes a good 5 The noaon as presened s smplfed by no usng dfferng noaons for he alpha and bea coeffcens across he specfcaons even hough hose would obvously dffer across he specfcaons. 6 Oher specfcaons ncludng varyng forms wh lagged dependen varable or ARMA models could be consdered; he specfcaons we used reflec our e ane deermnaon o focus on he role of ndvdual ndcaors and he esmaed ndcaor-specfc relaonshps for makng predcons of he dependen varable.

10 llusraon of he poenal for alernave specfcaon choces and he way he sysem works and also s conssen wh a prncple of parsmony. Choosng he Sample: Ieraons hrough Rollng Sample Szes The sysem uses nesed IF-THEN-ELSE saemens by varable o compare he predcon performance for specfcaons across sample szes and hen chooses he bes equaon by sample and by specfcaon. The eraons across sample szes sar from a mnmum sample of a leas 28 quarers up o a mamum of 101 quarers; whle hese parameers are somewha subjecve he mnmum sample sze conans daa from across a busness cycle a leas and he mamum covers up o weny-fve years of daa currenly as far back as The bes relave predcon performance s deermned by he lowes mean absolue error for he predced values of real GDP growh for an egh-quarer perod pror o he curren quarer. Furher because n real me esmaes for real GDP growh n recen quarers are ypcally prelmnary esmaes he mosrecen pror quarer s no ncluded n he egh-quarer predcon comparson perod. For eample f he sysem s generang a predced value for he second quarer of 2012 he eghquarer perod for predcon comparson ends wo quarer prevously he fourh quarer of Generang he Cenered Value -- Relave R-squared Weghng Afer he bes ndvdual ndcaor-specfc esmaes are deermned he sysem deermnes he cenered value for he esmae from he real-me sysem by weghng ndvdual ndcaor esmaes accordng o a relave R-squared weghng mehod usng he R-squared values from he chosen ndcaor-specfc esmang equaons. The wegh for he h ndcaor esmae for perod w for k ndcaors n he sysem s hen gven by: (1) w k R j1 2 R 2 j and he sysem esmae s gven by: (2) y ˆ w yˆ s k 1 where he subscrp s represens he sysem value and he ˆ y erm s he real GDP growh forecas for ndcaor deermned from he search across he alernave specfcaons as descrbed above. Noe ha he ˆ y esmaes and he w weghs wll vary hrough me and also can vary whn a perod as he daa avalably vares across (he jagged edge of) he curren 8

11 quarer (and as he program-deermned bes specfcaon poenally changes as well). Ths weghng mehodology gves greaer weghng o he ndcaor esmaes ha have a sronger hsorcal relaonshp n predcng real GDP growh and also assures he sum of he weghs wll be equal o 1.0. Noe ha a poenal alernave weghng mehodology could use he nverse of he mean absolue errors from he recen predcon comparson perod ha was used n he sysem o deermne he bes sample-specfcaon combnaon. Such an approach would deermne he weghs based on he recen predcon performance raher han he f over he hsorcal sample. Our nal eamnaon of resuls from he wo approaches ndcaes ha here s lle dfference beween he weghed predcons of hose wo approaches. 7 The Oupu Table The sysem code fnshes by wrng he oupu able lsng he ndvdual ndcaors and he sysem-generaed predced value for curren quarer real GDP growh. To provde addonal nformaon by ndcaor he oupu ncludes he R-squared for he esmaon equaon used; a number assgned o denfy he specfcaon employed; and he sample sze over whch he predcon equaon was esmaed. These resuls can be seen n he ables presened n Fgure 1 and are dscussed more n he ne secon. 4. Illusrave Resuls -- and Evoluon of Esmaes Durng a Quarer To llusrae he performance of he sysem Fgure 2 presens a collecon of s dfferen sysem oupu ables a varyng mes for makng esmaes for real GDP growh for he second quarer of The 24 varables n he sysem can be seen n he ables of Fgure 2. 8 The frs able n he upper lef shows an nal sysem esmae a he end of Aprl ha s a he end of he frs monh of he second quarer when only very nal observaons on any daa for he quarer could be observed. A ha pon he only daa avalable for he quarer (for he daa used n he sysem) were: nal and connung clams for unemploymen nsurance for he frs several weeks of Aprl; consumer confdence and consumer senmen for Aprl; he Phladelpha Fed busness acvy nde for Aprl; and he S&P500 sock nde for mos of Aprl. The daa hus represened only a very nal snapsho for he begnnng of he quarer. Tha s why s also very mporan ha he esmang and forecasng equaons from he sysem only use hsorcal daa for he frs monh of he hsorcal quarers and no full hree-monh quarerly 7 Sock and Wason [2006] dscuss alernave forecas combnng mehods ncludng relave hsorcal and forecas performance weghngs as shown and dscussed here. 8 An earler verson of hs paper was wren pror o he annual NIPA revsons n July 2012; hs verson was revsed afer he NIPA revsons. 9

12 Fgure 2-- Evoluon of Real-Tme GDP Forecass for 2012.Q2 BEA esmaes: Advance 1.5%; Revsed 1.7%; Fnal X.X% 10

13 daa properly accounng for he jagged edge. Alhough one would need o be cauous n nerpreng resuls from such a lmed nal se of daa he frs resul from he sysem a ha me showed a weghed esmae of abou 2.1 percen for real GDP growh n he second quarer. Such a resul could be nerpreed as he very nal daa ndcang ha real GDP growh was on rack o be posve and a a moderae rae. The sysem esmaes n he upper rgh of Fgure 2 show how he sysem esmaes changed as more daa came n over he subsequen weeks hrough he mddle May -- and noably now ncludng several of he more-recognzed daa repors on he economy for Aprl ncludng he Employmen Suaon release from he Bureau of Labor Sascs (BLS) ndusral producon and real sales. Wh ha addonal daa (bu agan only prmarly for he frs monh of he quarer) he sysem esmae for real GDP growh was a 2.4 percen. The ndvdual ndcaors generaed a farly large range of esmaes from 1.1 percen for he housng marke nde from he Naonal Assocaon of Home Bulders up o 4.05 percen from he S&P500 sock nde. By he begnnng of June (oupu able n mddle lef of Fgure 2) nal nformaon for a leas he frs monh was avalable for mos ndcaors and several ndcaors had begun o have a second monh as well. The sysem esmae for real GDP growh was a abou 2.2 percen wh a range across he ndcaors of 0.3 percen o 3.7 percen. By he end of June (able n mddle rgh of Fgure 2) -- he acual end of he second quarer bu sll when no all daa for he quarer were ye avalable -- mos of he ndcaor varables had wo monhs of daa for he quarer some had hree monhs (unemploymen clams consumer confdence and senmen and S&P500 nde) and a couple sll had only one monh (consrucon and epors). The sysem a ha me showed a weghed esmae of 1.97 percen. The fnal wo ables a he boom of Fgure 1 show he sysem esmaes a he end of July percen -- and a he end of Augus percen. A he end of July he BEA released he advance esmae of real GDP growh for he second quarer a 1.5 percen -- compared o he real-me sysem esmae of 1.8 percen a ha me and he marke consensus for 1.2 percen. By he end of Augus he BEA released s second esmae a 1.7 percen compared o he real-me sysem esmae of 1.8 percen and a marke consensus of 1.7 percen. By he end of Sepember he BEA released s fnal esmae of X.X percen for real GDP growh for he second quarer of In summary for hs secon he resuls and comparsons for he evoluon of sysem esmaes for he second quarer of 2012 llusrae how he sysem performed n provdng nformaon abou real GDP growh from a begnnng of a very lmed se of nformaon on few 11

14 ndcaors hrough he accumulaon of addonal nformaon across ndcaors unl nformaon for all monhs for all ndcaors was avalable -- and unl fnal esmaes from BEA were made. 5. Properes of he Esmaors Usng Curren-Vnage Daa Ths secon presens nformaon on he properes of he esmaes usng curren vnage daa; we use he curren-vnage daa n he absence of a long me seres of esmaes based on he conemporaneously-avalable real-me daa a he rollng hsorcal daa vnages a he nal observaon pons. Alhough some researchers may have a preference for usng hsorcal realme daa for evaluang he esmaes noe ha here s rarely (and somemes never) a pure apples-o-apples comparson for daa and analyss hrough me and especally relave o he observed daa a anoher pon n me hsorcally; daa defnons mehodologes sources ec. all change hrough me and ha s parcularly rue for an ndcaor such as real GDP growh ha s he focus of much of he aenon n real-me analyss. Hence for generang curren esmaes n real-me for he curren quarer here are srong argumens ha s bes o use relaonshps as denfed n he curren vnage of daa ha reflecs curren n-place mehods and consrucon. To eamne he properes of he sysem and ndcaor esmaes we ran he sysem o generae esmaes over he hsorcal perod from 1997.Q1 hrough 2011.Q4 usng curren vnage daa. Table 1 presens he RMSEs for he esmaes showng varous resuls ha wll be dscussed n urn. Of parcular noe he resuls n he lef hand sde of Table 1 show he resuls for he fleble esmaon sysem ha s he prmary focus of hs paper; hose on he rgh hand sde of Table 1 provde a comparson o a sysem n whch he specfcaons and sample horzons are fed. The op of he able presens resuls for sysem esmaes; he boom of he able shows resuls for ndcaor-specfc esmaes. Comparson for Sysem and Indcaor-Specfc Indcaors -- and a Subse of he Bes Indcaors The frs lne for he fleble sysem resuls (lef sde) shows he RMSE for he sysem esmae a 1.59 percenage pons whch compares favorably o he ndvdual ndcaor esmaes n he boom of he able where he lowes RMSEs are a 1.67 for durable goods orders and connung unemploymen nsurance clams. The sysem esmae also compares favorably o a nave rollng AR(2) auoregressve esmaon for whch he RMSE s 2.39 percenage pons as shown n he hrd lne. 12

15 An neresng queson s he een o whch he full sysem s beer han a small subse of ndcaors n makng he real-me esmae. The fourh lne shows he RMSE for an esmae usng an equally-weghed combnaon of he op 5 ndcaor esmaes 9 based on usng he fve ndcaors wh he lowes RMSE over he esmaon horzon -- for he fleble sysem hose bes ndcaors are (real) durable goods orders; connung unemploymen nsurance clams; (real) shpmens of durable goods; ndusral producon; and real real sales. An esmae based 9 We arbrarly chose o use he op fve o llusrae he small subse. 13

16 on hose fve ndcaors alone acually slghly ouperforms he full sysem esmae wh an RMSE of 1.53 compared o he 1.59 of he sysem. Tess Regardng he Properes of he Sysem Esmae Quesons reman abou oher properes of he esmaes noably unbasedness and n he sense dscussed n Debold and Lopez [1996]: The key propery of opmal forecas errors from whch all ohers follow s unforecasably on he bass of nformaon avalable a he me he forecas was made. To eamne hese quesons we conduced some smple regresson ess; he resuls are presened n Table 2. The frs equaon of Table 2 shows he resuls for regressng acual real GDP growh on he sysem esmae (usng ordnary leas squares); f he sysem esmae s an unbased predcor hen he jon hypohess ha he consan coeffcen s zero and he slope coeffcen s 1.0 should no be rejeced. The esmaed consan coeffcen s negave and sgnfcanly less han zero (a he fve percen level) and he slope coeffcen s sgnfcanly greaer han one; he F-sasc from a Wald es for esng he jon (01) hypohess s sgnfcan a 7.33 rejecng ha jon (01) hypohess. The second esmaed equaon of Table 2 goes furher regressng he fed error from he frs equaon on he one-quarer-lagged predcon error for he sysem esmae. If he sysem esmae msses he predcon n a gven quarer does ha carry nformaon for makng a predcon n he ne quarer? Tha s real GDP growh a mes ehbs a saw ooh paern -- f real GDP growh s abnormally large one quarer does real GDP growh end o be lower n he subsequen quarer? The esmaon resuls show ha he esmaed coeffcen on he pror quarer predcon error s sgnfcanly dfferen 14

17 from zero a he en percen level. Furher ncludng he lagged predcon error n he esmaed equaon (equaon 3 of Table 2) resuls n an esmaed coeffcen sgnfcan a he fve percen level and he F sasc of 6.77 shows ha he jon hypohess of (010) s rejeced. Alhough sn always he case ha he saw-ooh paern domnaes for he mes ha does he addonal role for he lagged predcor can be mporan so we nclude ha for makng an adjused esmae. Char 1 shows he hsorcal values for he alernave seres -- acual real GDP growh he (fleble) real-me sysem esmae and for he adjused seres ha accouns for he bas and he nformaon from he pror quarer predcon error. Char 1 shows ha he real-me sysem esmae ends o underpredc (absoluely) he more-ereme values for real GDP growh whereas he adjused measure does a beer job of capurng hose devaons from rend performance. Durng perods when real GDP growh s largely performng near rend -- such as occurred durng he lae-1990s and he md-2000s -- here s lle dfference n he esmaes. However noably durng recesson and low-growh perods he sysem esmae undersaes he een of GDP growh declnes whereas he adjused esmaes capure more of ha effec. Lookng back a Table 1 and he RMSEs for he alernave esmaes he second lne shows he lower RMSE for he adjused sysem esmaor a 1.38 compared o he 1.59 of he unadjused sysem esmae. We made an analogous adjusmen for he op 5 ndcaors esmae (resuls no shown); he ffh lne of Table 1 shows ha he RMSE s lower for he adjused 15

18 esmae for he op 5 case as well bu wh less relave mprovemen. The lower relave mprovemen apparenly s because he op 5 ndcaors end o be more volale o begn wh and end o do a somewha beer job durng he more ereme growh perods. In general he adjused sysem esmae yelds he lowes RMSE followed closely by he op 5 adjused esmae. In he eample presened above n secon 4 for he second quarer of 2012 he adjused esmae would be somewha lower a 1.3 percen compared o he fnal unadjused sysem esmae of 1.8 percen. Comparson o Fed Sysem Esmaes Fnally he rgh-hand-sde of Table 1 presens he equvalen se of RMSE numbers for runnng a verson of he sysem n whch he sysem s consraned o havng fed specfcaons and fed sample szes (80 quarers). 10 The fed sysem resuls almos unformly have hgher RMSE across he measures llusrang ha he fleble esmaon process yelds beer resuls for he sysem esmaes and for he ndvdual ndcaor-specfc esmaes (alhough here are a couple ecepons among he wors performng ndcaors n he boom of he able). 6. Oher Poenal Applcaons -- and a Monhly Payroll Jobs Esmaon Eample The mehodology and sysem employed here have many poenal applcaons beyond real-me esmaes of real GDP growh. We consder applcaons o: a resrced bes se of ndcaors verson of our sysem; an alernave approach wh separae sysem esmaes by GDP componen; specfc ndcaors or secors; and an llusraon of a verson of he sysem as appled o he monhly payroll jobs esmae from he BLS. An Alernave Mehodology: Usng a Subse of he Bes Indcaors Predcons As observed n he analyss of he pror secon a poenal refnemen o he mehodology would be o resrc he consrucon of he sysem esmae o a small subse of he ndcaors choosng o use a se of he ndcaor esmaes ha had he beer predcon performance. As observed such a change may no yeld esmaes ha are much dfferen from hose of he full sysem. In pracce our vew s ha we would end o use he full sysem esmae and use he op 5 esmaes o help nform our vews durng parcularly volale growh perods and noably near busness cycle urnng pons. Ye for many analyss and forecasers he resuls ndcae ha rackng he performance of hose key ndcaors may yeld mos of he nformaon ha could be gleaned from a larger more comprehensve se of ndcaors. Bu usng 10 The specfcaons were predeermned by subjecve e ane analyss by ndcaor. 16

19 a fleble esmaon approach such as n our sysem s also apparenly mporan for bes rackng he nformaon from hose ndcaors. An Alernave Mehodology: GDP by Componens Anoher alernave mehodology would be o apply he sysem esmaon procedures o an esmaon-by-componens approach for he componens of he accounng deny for nomnal GDP of: Y=C+I+G+(X-M). Such a mehodology could be promsng especally gven he challenges we have observed n repeaed use over me of he sysem esmaon noably ha he sysem may do parcularly well n esmang an aggregae ndcaor such as he change n prvae domesc real fnal sales. Tha s he sysem does less well n predcng real GDP growh when here are subsanal changes n more-eogenous componens such as changes n nvenores governmen spendng or ne epors. The frs quarer of 2011 s a noable eample; our sysem esmae oversaed real growh n ha perod as governmen spendng regsered a parcularly large declne. Such an approach would move more oward he bean counng accounng approach descrbed earler; a forecaser could use sysem-based esmaes by componen ndependenly or o augmen or serve as a check for he bean counng esmaes for curren quarer GDP growh. Alhough we have no conduced formal nvesgaon of hs approach we have observed ha makng real-me esmaes of some of he componens -- and noably governmen spendng -- s dffcul n pracce and could lm he ably o use he sysem n such an applcaon. Poenal Applcaons o Specfc Indusres Indees Cusom Measures The real-me sysem we descrbe n hs paper can poenally be appled o almos any seres for whch suffcen hsorcal daa es o esmae relaonshps o oher ndcaors. Obvous canddaes are he major monhly macroeconomc varables such as: ndusral producon durable goods orders and shpmens payroll jobs and he unemploymen rae ec. For eample Parg Golnell and Bodo [2010] use a real-me nowcasng approach for shorrun predcons of ndusral producon for Ialy. In fac n he ne secon we llusrae jus such an applcaon o he monhly payroll jobs esmae from he BLS. Before urnng o ha we noe ha he poenal also ess o consruc specal ndees or measures for a gven ndusry or ndusres or even a gven frm and hen use he sysem o regularly updae esmaed performance/acvy based on he sysem s esmaed relaonshps and ha would hen evolve auomacally hrough me. One can even magne usng an appled verson of he sysem o make esmaes of a performance measure for a frm or ndusry ha s unobservable n real me 17

20 and ha may no be drecly observable unl afer a subsanal lag of me (for eample poenally even a year or more). An Applcaon o Monhly Payroll Jobs Esmaon To llusrae how our real-me forecas sysem can be appled o an alernave economc ndcaor oher han real GDP growh we rewroe he EVews code o apply o one of he moremporan and well-known economc ndcaors he monhly payroll jobs esmae from he BLS. Gven he closer machng of monhly frequences for mos of he eplanaory ndcaors used and he dependen varable of he payroll jobs ndcaor he man dfferences n he EVews code were o elmnae he nesed loops for makng sure he daa for he proper monh(s) of he quarer were used and makng he code apply o a sngle monh raher han mulple monhs and quarerly averages. Also we used a subse of key economc ndcaors ha are ypcally or ofen avalable pror o he release of he Employmen Suaon repor and have a suffcenly long me seres. Hence we use daa on nal and connung unemploymen nsurance clams he employmen measure from he Phladelpha Fed s busness oulook survey consumer confdence and senmen he S&P500 nde ndees on busness acvy and employmen from he Insue for Supply Managemen (ISM) and he ADP employmen repor. Some of hese seres are avalable n he weeks of he monh pror o and leadng up o he Employmen Suaon release (unemploymen nsurance clams he S&P 500 nde consumer senmen Phladelpha Fed nde) ohers are only avalable closer or mmedaely before (consumer confdence revsed consumer senmen ADP) and somemes some of hese ndcaors are released jus before or poenally no released pror o he Employmen Suaon (ISM survey measures). Ths group of ndcaors s generally well-known as he key se of monhly ndcaors avalable pror o he Employmen Suaon and many are used by analyss and forecasers o nform her personal esmaes for payroll jobs growh n advance of he release of he esmaes. Agan one of he key aspecs of our analyss s he sysem s compuer program and code ha allow he fleble and (almos) nsananeous updang and daa-deermned choces of emprcal specfcaons and sample horzons as esmaes would be made and for an ongong process of makng payroll jobs esmaes from monh o monh Because of he large number of eraons and loops o compare alernave specfcaons and samples he Evews program for he real-me sysem for monhly payroll jobs esmaes requres jus over 3 mnues o run on a Dell T3500 compuer wh an Inel Xeon 3.20 GHz processor and a Wndows 7 operang sysem. Analogously for he real GDP sysem he me requred for he sysem o run s abou seven and a half mnues. 18

21 Fgure 3 -- Evoluon of Real-Tme Forecass for Payroll Jobs for May 2012 Noe: Inal BLS esmae June 1 s ; Fnal revsed esmae a Augus 3 rd. 19

22 Smlar o he analyss for he evoluon of he sysem esmae for real GDP we presen he evoluon of esmaes across a monh for payroll jobs for May 2012 (Fgure 3). Noe ha he jagged edge phenomenon and duraon are grealy reduced n hs applcaon spannng one monh raher han he hree monhs of he quarer for he real GDP applcaon. The frs able n he upper lef of Fgure 2 shows an nal sysem esmae n he mddle of May (May 18h) when only very nal observaons on any daa for he monh were observed: daa on nal and connung clams for unemploymen nsurance for he begnnng weeks of May; he prelmnary esmae for consumer senmen for May; he Phladelpha Fed nde employmen measure; and he S&P500 sock nde for he frs half of May. The daa hus represened an nal snapsho for May bu wh key daa on unemploymen nsurance clams avalable by ha me. The sysem s nal esmae a ha me was for payroll jobs growh of jobs. The sysem esmaes n he upper rgh of Fgure 3 show how he sysem esmaes changed over he followng week (hrough May 25 h ) as more daa came n alhough no subsanal changes wh he sysem esmae rsng only slghly o By May 29 h (mddle lef able of Fgure 2) consumer confdence was avalable (and yeldng a very low negave esmae) pullng down he sysem esmae o By he end of May (May 31 s ) he mddle rgh able shows ha he addon of he ADP esmae for May (a ) yelded he hghes ndcaor-specfc esmae a jobs and rased he sysem esmae o Noe hs was a monh when he ISM daa were no avalable pror o he Employmen Suaon release. The marke consensus durng hs perod pror o he ADP release was for an ncrease n payroll jobs of wh a range of o On June 1 s he BLS released s frs esmae for payroll jobs growh n May a Hence n he comparson of hs eample for May 2012 he real-me sysem esmaes of job growh lower han and well below he consensus -- were correc and relavely beer han he marke consensus. However even he relavely-low esmaes of (pre ADP) and (pos ADP) from he sysem were hgh compared o he BLS nally-repored The sysem esmaes n he boom of Fgure 3 nclude he daa on he ISM manufacurng employmen nde (boom lef) released on June 1 s afer he Employmen Suaon release and he ISM non-manufacurng busness acvy and employmen ndees (boom rgh) released on June 5 h. The esmae from he sysem wh all ndcaors ncluded s for jobs for May sll above he nal BLS esmae bu sll n he boom of he range of he prvae marke predcons ced above and much closer han he consensus. Wh subsequen revsons n he June and July repors he payroll jobs change for May was a closer o he sysem esmae. 20

23 7. Wha s he Useful Informaon n hese Esmaes? For he real-me GDP esmaes he esmaes are probably bes vewed as measurng he underlyng performance of GDP growh of underlyng growh n he economy. Ofen very specal even dosyncrac changes o componens wll yeld a real GDP growh number for a specfc quarer ha s que dfferen from he overall underlyng performance. Whle here s poenally lmed value n correcly predcng a one-me low or hgh value when he economy s growng a a fundamenally dfferen rae noneheless would sll be of value o undersand f here were specal facors ha resuled n an esmae beng parcularly hgh or low. The Lamp Pos Problem and Prvae Domesc Acvy The behavor of emporarly hgh or low quarerly growh esmaes n real me also hghlghs some of he challenges of makng such esmaes n our framework and mehodology. The effecve weghng s deermned by he relave performance of he fs of he equaons he R-squareds bu n pracce ha may resul n lower weghng for mporan varables for consrucng he real GDP growh esmae. Ths s a verson of he lamp pos problem ha he daa and resulng equaons beng used are he ones ha can be readly observed and hrough me whle dosyncrases and specal facors ha are more dffcul o observe could move he curren quarer esmae relave o wha s he ypcal relaonshp over hsory. The observable nformaon may poenally be beer n many perods a measurng prvae domesc acvy -- sudden shfs n ne epors and governmen are parcularly dffcul o capure. However hs s no a unversal generalzaon as varous quarers hsorcally had ouszed changes n real prvae domesc fnal sales ha were dffcul o predc (noably around he deepes pars of he recen recesson). Noneheless beng able o denfy when a parcularly low value or hgh value for a quarer s a fundamenal change n underlyng performance would be of parcular value for busness nformaon and polcy purposes. Informaon by Secor The dealed ndcaor-specfc esmaes from he real-me esmaon sysem provde nformaon on how specfc ndusres or secors are performng gven her hsorcal relaonshp o real growh n he economy. For eample wha are he esmaes and he relave magnudes from real economy ndcaors or from labor marke ndcaors or from senmen and survey daa? Those esmaes and relaonshps can provde poenally useful nformaon on he relave performance of dfferng pars of he economy. Addonal research could eamne for eample 21

24 wheher senmen vs. real acvy dspares carry addonal useful nformaon abou he curren or epeced fuure performance of he economy. 12 Relably of he Esmaes and he Daa The prelmnary naure of nal and subsequen esmaes for real GDP growh -- and he relavely long me before such esmaes go hrough annual or comprehensve revsons -- hghlghs some of he challenges of forecasng real GDP growh. Wha confdence do we have ha he repored values of real GDP growh are properly capurng he rue performance of he economy n real me? Or could be ha he real-me esmaes from a sysem such as ours could n fac gve a more useful measure of underlyng performance because of he drec e o he broad se of underlyng daa and no beng ed o he accounng framework and assocaed nal daa lmaons for he formal esmaes? The broader quesons of such challenges are beyond he scope of hs paper bu we wll noe ha he BEA publshes a se of comparsons for revsons o GDP n s nal (advance) esmaes for a quarer. For eample n s January 2012 release for s esmaes of GDP for he fourh quarer of 2011 he BEA repored ha for real GDP he average devaon whou regard o sgn of he advance esmae o he fnal (pos annual and comprehensve revson) esmae for he percen change was 1.3 percenage pons and wh a sandard devaon of 1.0 percenage pons (for comparsons for he perod 1983 o 2008). 13 Hence subsanal uncerany ess n real me regardng an acual pon esmae even for he governmen s formal esmae of he rae of real GDP growh. A separae broad-se-ofndcaors-based performance measure based on hsorcal relaonshps o real GDP growh can herefore poenally provde addonal useful nformaon n real me regardng he underlyng performance of he economy. An analogous challenge ess for he formal BLS esmaes for payroll jobs growh n real me as he jobs growh esmaes are subjec o nal monhly revsons for wo monhs and hen laer annual benchmark revsons ha can lead o subsanal changes n he monh-o-monh esmaed changes. Oher Hgh Frequency and Socal Meda Daa Wh he ncreased use of nerne search engnes and socal meda over he pas decade and he avalably of nformaon regardng her use he prospecs for usng hgh frequency and hgh volume daa from hose sources appear aracve n erms of ganng addonal nformaon 12 Relaed o hs Gannone Rechln and Smonell [2009] address he role of confdence ndcaors n real-me esmaon for Euro area real acvy. 13 The RMSE of 1.3 percenage pons for our adjused sysem esmae compares relavely well o hose BEA devaons. 22

25 n real me abou he behavor of he economy and key acors such as consumers and nvesors. Cho and Varan [2009] for eample eamne daa on search engne searches and relaed economc daa and clam ha Google Trends may help n predcng he presen and Bollen Mao and Zeng [2011] analyze he e conen of daly Twer feeds and fnd ha ha he accuracy of [Dow Jones ndusral average] predcons can be sgnfcanly mproved by he ncluson of specfc publc mood dmensons. We have made effors o use varous hgh frequency daa n he real-me sysem bu have no observed much success. In general he nformaon ganed from such sources s very nosy and s dffcul o denfy a srong-enough sgnal for generang sgnfcan eplanaory power for he aggregae economc varables of neres and especally n erms of provdng addonal eplanaory nformaon beyond he varables we already nclude n he sysem. Furher our analyss requres a suffcenly-long hsorcal me seres o esmae he relaonshp of he seres o he aggregae economc varable of neres. Whle here may be useful nformaon n hgh frequency and socal meda seres a hs me we have no been able o relably denfy or ncorporae addonal robus and sgnfcan eplanaory nformaon n our sysem. 8. Concludng Observaons The fleble real-me forecasng sysem presened n hs paper provdes a useful analycal ool for generang ongong daa-based nowcass of real GDP growh. The predcon errors for he sysem esmaes over a hsorcal perod compare favorably wh hose of ndvdual ndcaors and he fleble naure of he sysem -- allowng he daa o decde he specfcaons and sample horzons for esmaons -- yelds mproved predcon performance relave o esmaons wh fed specfcaons and sample horzons. Also whle he full sysem esmaes adjused for observed bas and neffcency produced he lowes roo mean square errors he evdence suggess ha a small subse of key ndcaors does almos as well as he full sysem esmae parcularly for perods of more ereme real GDP growh performance. The analyss ndcaes ha forecasers can poenally glean useful nformaon from applyng such an approach n pracce for makng real GDP growh esmaes; furher hey may be able o do so relavely well wh a small se of key ndcaors. The analyss also demonsraed he opporunes for applyng he mehodology o oher ndcaors by converng he sysem o eamne real-me esmaes for he monhly change n payroll jobs. In he end alhough challenges es for applyng he sysem for makng predcons n pracce he analyss and evdence presened n hs paper ndcae ha he sysem can provde poenally useful real-me nformaon abou real GDP growh and oher key economc varables. 23

26 References Angeln Elena Gonzalo Camba-Mendez Domenco Gannone Lucreza Rechln and Gerhard Rünsler 2011 Shor-Term Forecass of Euro Area GDP Growh. The Economercs Journal February. Bollen Johan Huna Mao Xao-Jun Zeng 2011 Twer mood predcs he sock marke Journal of Compuaonal Scence March. Bullgan Gudo Robero Golnell and Guseppe Parg 2010 Forecasng Monhly Indusral Producon n Real-Tme: From Sngle Equaons o Facor-Based Models. Emprcal Economcs Volume 39 Number Cho Hyunyoung and Hal Varan 2009 Predcng he Presen wh Google Trends unpublshed manuscrp Google Inc. Aprl 10. Blue Chp Economc Indcaors 2012 Aspen Publshers Vol. 37 No. 5 May 10. Debold Francs X. and Jose A. Lopez 1996 Forecas Evaluaon and Combnaon NBER Technal Workng Paper No. 192 March 1996 publshed n Handbook of Sascs 14: Sascal Mehods n Fnance eded by G.S. Maddala and C.R. Rao Amserdam: Norh-Holland. Drechsel Kaja Lauren Maurn 2011 Flow of Conjuncural Informaon and Forecas of Euro Area Economc Acvy Journal of Forecasng Volume 30 Issue 3 Aprl. Evans Marn D.D Where Are We Now? Real-Tme Esmaes of he Macroeconomy Inernaonal Journal of Cenral Bankng Sepember. Ferrara Lauren Domnque Guégan and Parck Rakoomarolahy 2010 GDP Nowcasng wh Ragged-Edge Daa: A Sem-Paramerc Modelng Journal of Forecasng. Gannone Domenco Lucreza Rechln and Davd Small 2008 Nowcasng: The Real-Tme Informaonal Conen of Macroeconomc Daa Journal of Moneary Economcs Volume 55 Issue 4 May Gannone Domenco Lucreza Rechln and Savero Smonell 2009 Nowcasng Euro Area Economc Acvy n Real-Tme: The Role of Confdence Indcaors Naonal Insue Economc Revew Sepember. Golnell Robero and Guseppe Parg 2008 "Real-me squared: A real-me daa se for real-me GDP forecasng" Inernaonal Journal of Forecasng Elsever vol. 24(3) Kchen John and Ralph Monaco 2003 Real-Tme Forecasng n Pracce: The U.S. Treasury Saff s Real-Tme GDP Forecas Sysem Busness Economcs Ocober. Parg Guseppe Robero Golnell and Gorgo Bodo 2010 "Forecasng Indusral Producon n he Euro Area" Emprcal Economcs Sprnger vol. 25(4) Rünsler Gerhard Karm Barhoum Szlard Benk Rcdardo Crsadoro Ard Den Rejer Audrone Jakaene Por Jelonek Anono Rua Karsen Ruh and Chrsophe Van Neuwenhuyze

27 Shor-Term Forecasng of GDP Usng Large Daases: A Pseudo Real-Tme Forecas Evaluaon Eercse. Journal of Forecasng Vol. 28 November. Sock James H. and Mark W. Wason 2006 Forecasng wh Many Predcors n Handbook of Economc Forecasng eded by G. Ello & C. Granger and A. Tmmermann Elsever Vol. 1 Chaper 10. Wagner Neal Zbgnew Mchalewcz Mouaz Khouja and Rob Roy McGregor 2005 Forecasng wh a Dynamc Wndow of Tme:The DyFor Genec Program Model n: Inellgen Meda Technology for Communcave Inellgence Lecure Noes n Compuer Scence. 25