EUI Working Papers DEPARTMENT OF ECONOMICS ECO 2010/06 DEPARTMENT OF ECONOMICS THE RELIABILITY OF REAL TIME ESTIMATES OF THE EURO AREA OUTPUT GAP

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1 DEPARTMENT OF ECONOMICS EUI Working Papers ECO /6 DEPARTMENT OF ECONOMICS THE RELIABILITY OF REAL TIME ESTIMATES OF THE EURO AREA OUTPUT GAP Massimiliano Marcellino and Albero Musso

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3 EUROPEAN UNIVERSITY INSTITUTE, FLORENCE DEPARTMENT OF ECONOMICS The Reliabiliy of Real Time Esimaes of he EURO Area Oupu Gap MASSIMILIANO MARCELLINO and ALBERTO MUSSO EUI Working Paper ECO /6

4 This ex may be downloaded for personal research purposes only. Any addiional reproducion for oher purposes, wheher in hard copy or elecronically, requires he consen of he auhor(s), edior(s). If cied or quoed, reference should be made o he full name of he auhor(s), edior(s), he ile, he working paper or oher series, he year, and he publisher. ISSN Massimiliano Marcellino and Albero Musso Prined in Ialy European Universiy Insiue Badia Fiesolana I 5 San Domenico di Fiesole (FI) Ialy cadmus.eui.eu

5 THE RELIABILITY OF REAL TIME ESTIMATES OF THE EURO AREA OUTPUT GAP Massimiliano Marcellino Albero Musso This version: 6 November 9 ABSTRACT This paper provides evidence on he reliabiliy of euro area real-ime oupu gap esimaes, including hose provided by he IMF, OECD and EC and a se of model based measures. A genuine real-ime daa se is used, including vinages of several ses of euro area oupu gap esimaes available from 999 o 6. I urns ou ha real-ime esimaes of he oupu gap are characerised by a high degree of uncerainy, much higher han ha resuling from model and esimaion uncerainy only. In paricular, he evidence indicaes ha boh he magniude and he sign of he real-ime esimaes of he euro area oupu gap are very uncerain. The uncerainy is mosly due o parameer insabiliy, while daa revisions seem o play a minor role. To benchmark our resuls, we repea he analysis for he US over he same sample. I urns ou ha US real ime esimaes are much more correlaed wih final esimaes han for he euro area, daa revisions play a larger role, bu overall he unreliabiliy in real ime of he US oupu gap measures deeced in earlier sudies is confirmed in he more recen period. Key words: Oupu gap, real-ime daa, euro area, daa revisions. JEL classificaion codes: E, E7, E5, E58. Marcellino: European Universiy Insiue, Bocconi Universiy and CEPR, massimiliano.marcellino@eui.eu. Musso: European Cenral Bank, albero.musso@ecb.in. We hank, wihou implicaing, Todd Clark for many useful suggesions. We are also graeful o Simon van Norden, Ken Wes, and paricipans o an ESCB seminar, he 5 h Eurosa Colloquium and a CES-IFO workshop for useful commens. All remaining errors are he sole responsibiliy of he auhors. The opinions expressed in his paper are hose of he auhors and do no necessarily reflec he views of he European Cenral Bank.

6 I. Inroducion Oupu gap measures are a key componen of a concepual framework which is very useful for he purposes of conjuncural and moneary policy analysis (see for example ECB,, and Mishkin, 7). Despie heir appealing characerisic as a relaively clear summary measure of overall slack in he economy, oupu gap esimaes are problemaic and represen a poenially misleading inpu in moneary policy analysis. The wo main problems in inerpreing and assessing he implicaions of broad summary measures of slack such as he oupu gap relae o he uncerainy surrounding he corresponding esimaes and he uncerain links beween hese measures and inflaion. Alhough evidence based on real-ime daa exiss for a number of counries, no such evidence exiss for he euro area. Agains his background, he aim of his paper is o provide updaed evidence on he uncerainy characerising euro area oupu gap real-ime esimaes, and compare i wih he case of anoher large common currency area, namely, he US. Recen empirical sudies for he US, UK and Canada have shown ha he problem of oupu gap measuremen uncerainy is paricularly severe for real-ime esimaes (ha is, esimaes of he oupu gap for he period when he acual esimaion is carried ou), which would ypically be hose of higher ineres for conjuncural and policy analysis (Orphanides and van Norden,, Nelson and Nikolov,, and Cayen and van Norden, 5). I has even been suggesed ha he mis-measuremen of he oupu gap in real ime may have conribued o wrong economic policy decisions in some counries in he pas (see for example Orphanides,, for he US and Nelson and Nikolov,, for he UK). For he euro area he evidence is more limied. A number of sudies have addressed he usefulness of euro area oupu gap esimaes in erms of revisions and inflaion forecasing performance. Overall, resuls appear o vary somewha across sudy. On he one hand, Michell (7) finds ha boh poin esimaes and measures of uncerainy (densiy esimaes) of euro area oupu gap esimaes are clearly unreliable, and Planas and Rossi () find ha esimaes of he oupu gap based on bivariae models (he bivariae Phillips curve-based model of Kuner, 99) do no exhibi a higher accuracy i.e. narrower confidence bands- relaive o esimaes based on univariae mehods (he unobserved componens model of Wason, 986). On he oher hand, Camba-Méndez and Rodríguez Palenzuela (), Proiei, Musso and Wesermann (7) and Rünsler () find ha esimaes of he euro area oupu gap based on mulivariae mehods (mainly mulivariae unobserved componens models) do no appear o be as unreliable as hose for he US. A he same ime, i is difficul o assess he resuls of hese papers in erms of usefulness of he euro area oupu gap for policy purposes as all of hem are based on one specific vinage (he laes available a he ime of he sudy). Since only recenly have real-ime daabases become available for he euro area, previous sudies could a mos be based on pseudo-real ime daa. In conras, he presen sudy uses a genuine se of real ime oupu gap esimaes for he euro area, which allows drawing more robus conclusions regarding he reliabiliy of euro area oupu gap esimaes, as well as comparing resuls wih corresponding ones obained for he US by Orphanides and van Norden () and ohers. Wih respec o he previous lieraure, as menioned, we presen a fully real ime evaluaion. In addiion, we compare a large se of oupu gap measures, including simple filer based esimaes relying on real GDP, measures based on capaciy uilizaion, esimaes based on mulivariae unobserved componen models, and a variey of esimaes from inernaional organizaions such as he IMF, OECD and European Commission. In addiion, we consruc

7 gap measures by averaging hose described so far. Averaging is a paricular way of pooling, and from he forecasing lieraure i is well known ha pooling, and in paricular averaging, a se of forecass can yield subsanial gains in erms of mean square forecas error reducion, see e.g. Sock and Wason (999). Moreover, averaging can reduce problems of parameer insabiliy and i is also a way o ake ino accoun mehod uncerainy, since here is no uniquely acceped or bes mehod o compue a gap, along he lines of Bayesian model averaging. The paper is srucured as follows. Secion describes he real ime daa and gap measures used. Secion repors summary measures of he uncerainy characerising euro area realime oupu gap esimaes. Secion compares he resuls on uncerainy wih hose for he US over a comparable sample period. Secion 5 summarizes he conclusions of our analysis. Addiional maerial and more deailed resuls are presened in Appendices. II. Daa I is possible o glean some insigh on he degree of uncerainy in genuine real-ime esimaes and projecions of he euro area oupu gap on he basis of esimaes published regularly since 999 by some major inernaional organisaions as well as esimaes based on euro area real-ime daa which has become available only recenly. In conras o previous sudies, he evidence repored in his paper is based on euro area oupu gap esimaes for which real ime vinages for a leas a few years are available. We consider five differen ypes of oupu gaps, which are compared o real GDP growh in real ime. Firs, measures based on capaciy uilizaion: he deviaions from he average value and from a linear rend. Since capaciy uilizaion figures are no revised, changes in he real ime vinages are only due o recursive esimaion of he mean of he variable, and of he slope of he linear rend. The daa are from he European Commission survey on he manufacuring secor. These measures are used as a driving force of he cyclical componen of he variables included in some of he more complex oupu gap models described below. They are included in he analysis as i migh be ineresing o assess wheher i makes a significan difference o use more complex oupu gap esimaes (wheher or no based also on hese capaciy uilizaion measures) relaive o using only hese simple measures of slack. Second, esimaes compued on he basis of he mulivariae unobserved componens (UC) model of Proiei, Musso and Wesermann (7), which combines a producion funcion and a Phillips curve equaion. We consider hree alernaive versions: he common cycle ( CC ) one, where all cyclical componens are driven by he cycle in capaciy uilisaion; he pseudoinegraed cycles ( PIC ) one, where all cyclical componens are driven also by idiosyncraic cycles; and he bivariae version ( BIV ), where he Kalman filer is applied direcly o oupu raher han o he componens of he producion funcion. Appendix I repors some deails on he alernaive specificaions of he UC model used, see Proiei, Musso and Wesermann (7) for addiional deails. An advanage of hese ypes of measures of oupu gap is ha i is possible o consruc and provide confidence inervals around he poin esimaes. Third, measures provided by inernaional organizaions. These include annual esimaes published wice a year by he European Commission (in he conex of heir annual Spring and Auumn forecass), he IMF (in he conex of he annual Spring and Auumn World Economic Oulook) and he OECD (in he conex of he annual June and December OECD

8 Economic Oulook). Noe ha he EC has wo ses of esimaes, one based on deviaions from a rend derived by applying he HP filer o each euro area counry series and hen aggregaing he resul ( EC-T ), and anoher represening deviaions from a rend esimaes wihin a producion funcion approach ( EC-P ), which was sared in. The IMF and he OECD gap measures are also based on a producion funcion approach. Fourh, measures obained by applying sandard filers o he real GDP levels. In paricular, we consider he HP filer ( HP ), he Baxer and King (999) band-pass filer ( BP ), and deviaions from a linear rend ( LIN ). In order o reduce he impac of he so-called end-ofsample bias we exend each vinage of real GDP daa via a simple AR() model (applied o he year-on-year growh rae), apply he filers o he exended levels and finally, as suggesed by Baxer and King (999), we disregard he las hree years of filered daa. For he HP filer we use a smoohing coefficien (lambda) of 6, as was suggesed by Hodrick and Presco (997) for quarerly daa and as is ypically done in he lieraure, while for he bandpass filer we use he cu-off frequencies suggesed by Baxer and King (989), i.e. we keep only he componens of he daa beween he cu-off frequencies beween.5 and 8 years. Nowihsanding he well-known problems wih hese filers, hey are sill fairly common in empirical applicaions, see e.g. Wason (7) for a criical review. In our conex, hey are convenien o isolae he effecs of wo sources of changes in oupu gap vinages: recursive esimaion and changes in he vinages of real GDP. In paricular, we can compue pseudoreal ime gaps using recursively he final vinage of real GDP daa, in addiion o ruly real ime gaps ha are recursively based on he real ime vinages of real GDP daa. The difference beween hese wo ypes of gaps is purely due o changes in real ime vinages of real GDP. Fifh, we consruc gap measures by averaging some of hose in groups -. Averaging is a paricular way of pooling, and from he forecasing lieraure i is well known ha pooling, and in paricular averaging, a se of forecass can yield subsanial gains in erms of mean square forecas error reducion, see e.g. Sock and Wason (999). Moreover, averaging is also a way o ake ino accoun mehod uncerainy, since here is no uniquely acceped or bes mehod o compue a gap, along he lines of Bayesian model averaging. We consider five averages: of all gaps in groups - ( Average All ), of hose belonging o he producion funcion approach ( Average PFA, including CC, PIC, EC-P, IMF and OECD), of hose from inernaional organizaions ( Average Org, including EC-T, EC-P, IMF and OECD), of hose from he UC models ( Average UC, including CC, PIC and BIV) and of hose from he sandard filers ( Average Filers, including HP, BP and LIN). I is also worh menioning ha, in order o consruc a se of quarerly vinages of quarerly esimaes, he following seps were underaken when needed: For hose vinages for which daa before 99 was no available, esimaes were exended backwards using (he changes in) he previously available hisorical vinage from he same source, or he closes subsequenly available hisorical vinage if previous vinages also lacked hisorical daa. Annual daa were inerpolaed o derive quarerly series. We compared alernaive approaches, which produced similar resuls likely because few daa poins are inerpolaed and he source daa is fairly smooh. In he end, we fied a local quadraic polynomial for each observaion of he annual series, and hen used his polynomial o fill in all observaions of he quarerly series associaed wih he period. The quadraic

9 polynomial is formed by aking ses of hree adjacen poins from he source series (wo for end-poins) and fiing a quadraic so ha he average of he quarerly poins maches he annual daa acually observed. To consruc he quarerly daabase, he laes available biannual vinage was used o represen he quarerly vinage. Thus, for example, he IMF Spring esimaes of (which became available in April ) were used o represen he Q and Q vinages, while he Auumn esimaes of (which became available in Ocober ) were used o represen he Q and Q vinages. Table summarises he characerisics of he oupu gap esimaes used in he paper. Overall, 9 o vinages are available, depending on he se of esimaes. Appendix II shows all vinages of all esimaes used. Table Vinages of euro area oupu gap esimaes Daa and esimaes* Definiion of rend Sample period** Frequency*** Vinages Source Real GDP 985Q-6Q quarerly daa Q-7Q ( 6 ) EABCN Capaciy uilisaion rae Average 985Q-6Q quarerly daa Q-7Q ( 6 ) European Commission Capaciy uilisaion rae Linear rend 985Q-6Q quarerly daa Q-7Q ( 6 ) European Commission UC - CC Prod Fn Approach 985Q-6Q quarerly daa Q-7Q ( ) own esimaes UC - PIC Prod Fn Approach 985Q-6Q quarerly daa Q-7Q ( ) own esimaes UC - BIV Bivariae model 985Q-6Q quarerly daa Q-7Q ( 9 ) own esimaes EC - Trend HP rend 985Q-6Q annual daa 999Q-7Q ( ) European Commission EC - Poenial Prod Fn Approach 985Q-6Q annual daa Q-7Q ( 9 ) European Commission IMF Prod Fn Approach 985Q-6Q annual daa 999Q-7Q ( ) IMF OECD Prod Fn Approach 985Q-6Q annual daa 999Q-7Q ( ) OECD Band-pass filer Sochasic rend 985Q-6Q quarerly daa Q-7Q ( 6 ) own esimaes Hodrick-Presco filer Sochasic rend 985Q-6Q quarerly daa Q-7Q ( 6 ) own esimaes Linear rend filer Linear rend 985Q-6Q quarerly daa Q-7Q ( 6 ) own esimaes Source: EABCN, EC, IMF, OECD and own esimaes. Noes: Real GDP daa are from he EABCN (see Giannone e al., 8, for deails). * EC, IMF and OECD publish biannual esimaes. To consruc he quarerly vinages for each quarer he laes available vinage is used. ** Each vinage available a ime T includes daa from 985Q o T-. For hose vinages for which no daa prior o 99 was available esimaes have been exended backwards using he (changes of he) previously available hisorical esimae (or if no available he firs subsequen esimae). *** Annual daa were inerpolaion via quadraic mach average opion of Eviews o derive quarerly esimaes. III. Uncerainy characerising euro area real-ime oupu gap esimaes In his Secion we provide a horough evaluaion of he uncerainy characerising euro area oupu gap esimaes, which sems from various sources. In he firs subsecion we focus on model uncerainy. In he second subsecion on parameer esimaion uncerainy. In he hird subsecion on parameer insabiliy. And in he final subsecion on he role of daa revisions. To evaluae he expeced size of he inerpolaion error, we have aggregaed he las vinage of he quarerly CC gaps o annual daa, and applied he inerpolaion mehod described in he ex o obain inerpolaed quarerly values of CC. The correlaion beween he acual and inerpolaed values of CC is higher han.98. Linear or cubic inerpolaion resuled in correlaion values around.9. 5

10 III.. Model uncerainy A basic problem in he esimaion of he oupu gap is ha several alernaive mehods have been proposed o esimae i, each wih is own advanages and disadvanages, bu here is no broad consensus on which approach should be adoped. Moreover, differen mehods end o produce significanly differen esimaes (his source of oupu gap uncerainy is hus someimes called model uncerainy ). Table summarises he main feaures of he slack measures considered wih reference o he final esimae (we ake as final esimae he las vinage available in our daa se; needless o say, hese esimaes are likely o be furher revised bu we follow he convenion of using he las available vinage as he closes approximaion o wha can be hough of as final esimaes). All measures exhibi some similariy, noably a high degree of persisence, as indicaed by values of he firs order auocorrelaion index beween.89 and.98. However, clear differences can also be deeced. For example, he mean of hese esimaes, which apar from GDP growh could be expeced o be zero, is clearly significanly differen from zero in some cases. In par his is due o he fac ha we repor he mean for he period 985-6, while in some cases daa is available for a longer period and in oher cases he laes esimaes are available for a shorer period and had o be exended backwards wih previous vinages as explained in he previous secion. However, his could also be aken as an indicaion ha some measures may provide less appropriae esimaes of he oupu gap, as for example in he case of deviaions of real GDP from a linear rend (given he likely sochasic naure of he underlying rend). Accordingly, also he variabiliy of hese esimaes ends o differ somewha, wih sandard deviaion measures in some cases being wice as large as in oher cases. This is of course in par relaed o he differen mean of he series. Moreover, he range of flucuaions appears o differ significanly across esimaes. Table Euro area oupu gap summary saisics mean s dev min max AR GDP growh Cap. uil. rae (dev. av.) Cap. uil. rae (dev. lin. rend) UC-CC UC-PIC UC-BIV EC (dev. from rend) EC (dev. from poenial) IMF OECD Band-Pass Filer HP Filer Linear Filer Average All Average PFA Average UC Average Org Average Filers Noes: Sample period is 985: o 6: in all cases. AR refers o he firs order auocorrelaion coefficien. 6

11 Differences in esimaes can also be significan wih regards o specific poin esimaes (see Char, based on laes vinage daa). I is far from rare ha some esimaes poin o a posiive oupu gap in a specific quarer or year, while oher esimaes poin o a negaive one. This seems o be he case for boh final esimaes (Char ) and for real ime esimaes (Char ). For example, among he oupu gap esimaes (i.e. hose based on he UC and filers and from he EC, IMF and OECD), he average difference beween he maximum and he minimum of final esimaes from 998 o 6 is.5 percenage poins, wih a peak (found in 6Q) of.5 percenage poins. Over he same period, he corresponding average range for real ime esimaes was.6 percenage poins, wih a peak (found in Q and Q) of.6 percenage poins. Moreover, in % of he cases for he final esimaes from 998 o 6 (and % from 985 o 6) he minimum and he maximum have differen signs. For he real ime esimaes from 998 o 6 a differen sign is found in % of he cases. I should be recognised ha he variaion across esimaes also derives from he differen ses of projecions for he daa used o esimae he gap across insiuions, and herefore model uncerainy is no he only source of variaion. Char : Final esimaes of euro area oupu gap and oher slack indicaors (percenage deviaions from rend/poenial oupu/average) GDP gr. CU-Tr UC (PIC) CU-Av UC (CC) UC (BIV) EC-Tr EC-Po IMF OECD HP BP LIN Q 998Q 999Q 999Q Q Q Q Q Q Q Q Q Q Q 5Q 5Q 6Q 6Q - 998Q 998Q 999Q 999Q Q Q Q Q Q Q Q Q Q Q 5Q 5Q 6Q 6Q Sources: EABCN, European Commission, IMF, OECD and own esimaes. Noe: UC: Esimaes from he mulivariae unobserved componens model of Proiei, Musso and Wesermann (7). The versions of he UC model shown are he common cycles varian (CC), he pseudo-inegraed cycles varian (PIC) and he bivariae (BIV) varian respecively. The range from 985 o6 was.9 pp, wih a peak of. pp in 99Q. 7

12 Char : Real ime esimaes of euro area oupu gap and oher slack indicaors (percenage deviaions from rend/poenial oupu/average) GDP gr. CU-Tr UC (PIC) CU-Av UC (CC) UC (BIV) EC-Tr EC-Po IMF OECD HP BP LIN Q 998Q 999Q 999Q Q Q Q Q Q Q Q Q Q Q 5Q 5Q 6Q 6Q - 998Q 998Q 999Q 999Q Q Q Q Q Q Q Q Q Q Q 5Q 5Q 6Q 6Q Sources: EABCN, European Commission, IMF, OECD and own esimaes. Noe: UC: Esimaes from he mulivariae unobserved componens model of Proiei, Musso and Wesermann (7). The versions of he UC model shown are he common cycles varian (CC), he pseudo-inegraed cycles varian (PIC) and he bivariae (BIV) varian respecively. I can be noiced ha uncerainy in oupu gap esimaes ends o be more significan han uncerainy characerising real GDP growh. Alhough revisions in real GDP growh are occasionally non-negligible (Char ) revisions in oupu gap esimaes end o be clearly more marked (see for example Char and Appendix II for more examples). Char : Vinages of euro area real GDP growh (percenages, year-on-year growh) Char : Vinages of euro area oupu gap esimaes by he IMF (percenage deviaions from poenial oupu) Q 99Q 99Q 99Q 995Q 996Q 997Q 998Q 999Q Q Q Q Q Q 5Q 6Q GQ GQ GQ GQ GQ GQ GQ GQ GQ GQ GQ GQ GQ GQ GQ GQ G5Q G5Q G5Q G5Q G6Q G6Q G6Q G6Q G7Q G7Q 99Q 99Q 99Q 99Q 995Q 996Q 997Q 998Q 999Q Q Q Q Q Q 5Q 6Q Sep- Nov- Feb- May- Sep- Dec- Feb- Jun- Sep- Dec- Mar-5 Jun-5 Sep-5 Dec-5 Mar-6 Jun-6 Sep-6 Dec-6 Mar-7 Jun-7 Sources: EABCN. Sources: IMF. 8

13 III.. Parameer uncerainy Anoher source of uncerainy resuls from he fac ha each mehod requires he esimaion of one or more parameers, which are unobserved and may change over ime, for example as a resul of srucural change. Given he limiaions of available esimaion echniques and he relaively shor sample periods available for many variables, parameers end o be esimaed wih a significan degree of uncerainy (his source of uncerainy is associaed wih wha is ofen called parameer uncerainy ). One way o assess uncerainy which, o some exen, can be associaed o parameer uncerainy is by compuing and examining confidence bands around poin esimaes. These are ypically no published (and herefore are no available for he esimaes from he inernaional organisaions). An idea of he magniude of parameer uncerainy for euro area oupu gap esimaes can be derived from confidence bands of UC esimaes, compued as plus and minus wice he sandard errors, as shown in Char 5. For example, for he mulivariae UC models, alhough he widh of he confidence bands ends o vary over ime and across esimaes (wih an average beween 98 and 6 of.7pp for he common cycles model and.8pp for he pseudo-inegraed cycles model), i ends o be paricularly high around urning poins, for real-ime esimaes, which are precisely hose of highes ineres from a policy perspecive. Char 5: Esimae of euro area oupu gap and corresponding confidence bands according o a mulivariae unobserved componens model (percenage deviaions from poenial oupu) Mulivariae common cycles model Mulivariae pseudo-inegraed cycles model Bivariae model Sources: Own calculaions. Noe: Esimaes from he mulivariae unobserved componens model of Proiei, Musso and Wesermann (7). Confidence bands are compued as +/- wo sandard error. 9

14 III.. Parameer insabiliy A hird source of uncerainy abou oupu gap measures is represened by parameer insabiliy. To assess is relevance for he reliabiliy of gap measures, we have compued recursively bu using he final vinage of daa he filer based gaps (namely, HP, Band-pass and linear), wha is ypically called a pseudo real ime evaluaion. We have also compued recursively he capaciy uilizaion based gaps. Noice ha since his variable is no subjec o revisions, he pseudo real ime and he fully real ime gaps coincide. For he UC model based gaps, a pseudo real ime evaluaion would be based on he filered raher han smoohed esimaes using he final vinage of daa, bu unforunaely he filered values are no available. Similarly, pseudo real ime values for he gaps produced by inernaional organizaions are no available. Noice ha he correlaion beween he pseudo real ime esimae and he final is very high in he case of he capaciy-based measures, while i is insignifican in he hree filer-based esimaes, wih he excepion of he linear filer (Table ). The laer resul is likely due o he sensiiviy of he filer measures o he end of sample observaions and he difficuly of correcly forecasing hem. Table Pseudo real ime esimaes of he euro area oupu gap mean s dev min max AR corr sign Cap. uil. rae (dev. av.) Pseudo RT % Rev FP Cap. uil. rae (dev. lin. rend) Peudo RT % Rev FP Band-Pass Filer Pseudo RT % Rev FP HP Filer Pseudo RT % Rev FP Linear Filer Pseudo RT % Rev FP Noes: Sample period is : o 6: in all cases ( observaions). AR refers o he firs order auocorrelaion coefficien. Rev FP sands for revision final esimae minus (pseudo) real ime esimae. sign refers o he percenage of imes he pseudo real ime esimae has he same sign as he final esimae corr repors he correlaion beween pseudo real ime esimaes and final esimae in he Pseudo RT row and he correlaion beween pseudo real ime esimaes and he revision final esimae minus (pseudo) real ime in he Rev FP row.

15 III.. Daa uncerainy Real-ime esimaes of he oupu gap end o be revised significanly over ime no only for poenial parameer insabiliy bu also for a variey of reasons relaed o daa uncerainy. In paricular i is worh menioning he lack of daa for he mos recen period (for which ypically some preliminary esimae based on very limied informaion is used), revisions of published daa (which ypically is more subsanial for he mos recen daa), end-of-sample insabiliy (i.e., esimaes for he end of he sample period end o vary significanly wih he addiion of one or few observaions, independenly of daa revisions) and, for esimaes condiional on projecions of macroeconomic daa for he period ahead, revisions in he projecions. Since he effecs of daa uncerainy can differ across he alernaive gap measures, as well as hose of parameer insabiliy, we now compare he final esimaes evaluaed in Secion. wih fully real ime esimaes, compued recursively as in subsecion. bu using in each quarer he available vinage of daa. To sar wih, we consider differences beween final and real ime (yearly) real GDP growh, which provides an indicaion of he exen of daa revisions in he real GDP series ha underlies mos gap measures. Alhough quarerly growh raes are mos ofen he reference measure for conjuncural analysis, we focus here on annual growh raes as he laer have a more pronounced cyclical paern and are herefore ypically he reference measure for business cycle analysis and, accordingly, he res of he paper. We sress again ha in he paper final refers o he laes available vinage. From Table, here are some differences in he mean, sandard deviaion and range of final and real ime values for growh, which sugges posiive revisions of iniial values. However, he differences are no marked, and he correlaion beween he final and real ime series is abou.98 (see also Char ). As a consequence, he persisence of he series is similar,.88 versus.85, and hey always have he same sign. These resuls sugges ha revisions o he gap measures are no due o major revisions in he underlying real GDP series, a leas over he period under analysis, in line wih he graphical evidence provided earlier. Following Mankiw and Shapiro (986) and, more recenly, Arouba (8), one migh wan o consider wheher he revision process in he GDP growh rae is beer characerized by he noise or news models. In paricular, in he noise model preliminary daa are hough of as final daa subjec o a measuremen error, while in he news model preliminary daa are considered as forecass of final daa. Mankiw and Shapiro (986) sugges ha he wo hypoheses can be discriminaed by regressing eiher he final values on a consan and he preliminary values (regression a) or, vice versa, he preliminary values on a consan and he final values (regression b). Under he news hypohesis, he coefficien of preliminary values in he regression a should be equal o one, he consan should be equal o zero, and he coefficien of he final values in he regression b should be smaller han one. Similar resricions, wih he proper changes, should hold under he noise hypohesis. Unforunaely, our evaluaion sample is oo shor for a formal evaluaion of his issue. In paricular, when he noise or news hypoheses are esed wih a robus F-saisic, hey are boh rejeced. Arouba (8) explains ha his finding can be due o a non-zero revision error. However, when we remove he mean from he revision error, boh he news and he noise resricions are no rejeced. Hence, we ake a more informal approach and simply repor he correlaions beween he real ime and final values wih he revision error (he difference of final and real ime values). Under he noise hypohesis, he final value should be uncorrelaed wih he revision, while under he news hypohesis he real ime value should

16 be uncorrelaed wih he revision. From Table, he correlaion beween final and revision (.) is smaller in absolue value han ha beween real ime and revision (-.6), which provides some evidence in favour of he noise hypohesis. Camacho and Perez-Quiros (8) find similar values and reach a similar conclusion. For he UC model based gaps, he resuls repored in Table sugges ha CC has he highes correlaion beween final and real ime values,.96, followed by BIV,.7, and PIC,.5. The ranking in erms of percenage of same signs beween final and real ime is he same, wih % for CC and he lowes percenage for PIC, 75%, which means han one ou of four quarers he sign of he real ime gap is laer reversed. The larges revisions are insead for BIV, -.6 and.9. In erms of he revision process, i should be considered ha he gaps are in general obained hrough complicaed procedures so ha he revision error can be due o a variey of reasons, as menioned, in addiion o revisions in he underlying GDP daa. Hence, he applicabiliy of he news or noise models for he gap is quesionable. However, i can sill be of ineres o consider he correlaions beween final and real ime esimaes and he revision error, in paricular because his can affec he properies of gap based forecass (as discussed in Marcellino and Musso (9)). I urns ou ha here are large differences across mehods in hese correlaions, wih he lowes value in absolue erms for he correlaion beween he CC final and revision error (-.), and he larges value for ha beween he BIV final and revision error (.86). As regards he oupu gaps produced by EC, IMF and OECD, resuls are mixed. On he one hand he highes correlaion beween final and real ime esimaes is found for he OECD esimaes (.8) and he lowes for he esimaes by he EC based on he producion funcion approach (.9). However, he highes percenage of same signs beween final and real ime is found for he laer esimae (8%). The correlaion beween final esimaes and revisions ends o be high in all four cases, ranging from.78 (IMF) o.96 (EC, deviaions from rend). By conras, he correlaion beween real ime esimaes and revisions ends o vary significanly, from he lowes in absolue value (-.) for he IMF esimaes o he highes (.56) from he OECD. I can also be observed ha he range of real ime revisions ends o be larger compared o hose found for he UC model based gaps. Esimaes based on filers indicae a relaively high percenage of same sign beween real ime and final (85% in all hree cases considered), bu he correlaion beween hese wo esimaes is eiher very close o zero (BP and HP) or relaively low compared o he oher esimaes considered above (.6 for he linear rend deviaions). In all cases for he filer based esimaes correlaion of final and real ime esimaes wih he revision is relaively large, suggesing ha i is difficul o classify hese esimaes. The range of real ime revisions for hese esimaes is relaively high compared o he UC model based esimaes bu no relaive o he esimaes by he EC, IMF and OECD. Resuls for he esimaes based on pooling some or all of he above menioned esimaes, repored in Appendix III, sugges ha here does no appear o be any significan improvemen compared o he bes se of esimaes of each group, eiher in erms of correlaion of real ime esimaes wih he final esimaes, percenage of same sign or range of revision of real ime esimaes.

17 Table Revisions o real ime euro area oupu gap esimaes mean s dev min max AR corr sign GDP Final RT % Rev RT UC-CC Final RT % Rev RT UC-PIC Final RT % Rev RT UC-BIV Final RT % Rev RT EC (dev. from rend) Final RT % Rev RT EC (dev. from poenial) Final RT % Rev RT IMF Final RT % Rev RT OECD Final RT % Rev RT Band-Pass Filer Final RT % Rev RT HP Filer Final RT % Rev RT Linear Filer Final RT % Rev RT Noes: Sample period is : o 6: in all cases ( observaions). AR refers o he firs order auocorrelaion coefficien. Rev RT sands for revision final esimae minus real ime esimae. sign refers o he percenage of imes he real ime esimae has he same sign as he final esimae corr repors he correlaion beween real ime esimae and final esimae in he Final row, he correlaion beween real ime esimae and he revision (final minus real ime) in he RT row, and he correlaion beween final esimae and he revision (final minus real ime) in he Rev RT row.

18 In order o gain some insigh ino he sources of he revisions in real ime esimaes i can be useful o underake a decomposiion suggesed by Orphanides and van Norden (), based on a comparison of genuine real ime esimaes wih pseudo real ime esimaes, allowing o assess he relaive role of parameer insabiliy and daa uncerainy. Using our daase his can be implemened for he hree ses of esimaes based on filers. The impac of daa revision can be assessed by observing he difference beween genuine real ime esimaes and pseudo real ime esimaes. As suggesed by Char 6, in all cases he conribuion o he oal revision of daa revision is clearly minor over he sample period considered. These resuls sand in conras wih hose for he US repored by Orphanides and van Norden (), according o which daa revisions are no he major source of revision bu appear o play a more significan role compared o wha appears o be he case for he euro area. This resul could be parly explained by he differen sample size and evaluaion period, bu we will see in he nex Secion ha we find i even over a comparable sample. Thus, for he euro area i appears ha he main source of he oal revision in real ime esimaes is represened by he addiion of new daa poins o he daa sample over ime, raher han revisions o hisorical daa. The laer would appear slighly more imporan when measured on a quarer on quarer basis. Char 6: Real ime esimaes of euro area oupu gap, oal revision and daa revision (percenage poins) Band-pass filer esimaes HP filer esimaes RT esimaes oal revision daa revision RT esimaes oal revision daa r evision Q Q Q Q Q Q 5Q 5Q 6Q 6Q Q Q Q Q Q Q 5Q 5Q 6Q 6Q Linear rend filer esimaes RT esimaes oal revision daa revision Q Q Q Q Q Q 5Q 5Q 6Q 6Q Sources: Our calculaions.

19 The revisions of he euro area oupu gap real ime esimaes end o be significan (see Char 7). Revisions are ofen of he same (or even higher) magniude as he esimaed gap iself. This appears o be he case paricularly for some esimaes, such as hose by he IMF and hose based on he linear rend filer. By conras, revision of real ime esimaes based on he UC model appear be more limied, especially hose of he CC version. These revisions seem o be larger for he less recen years, bu i should be kep in mind ha he laes esimaes are subjec o furher changes, reflecing he above-menioned problem of end-of-sample insabiliy. Char 7: Revisions o real-ime esimaes of euro area oupu gap (differences beween laes and real-ime esimae) GDP gr. CU-Av CU-Tr UC (CC) UC (PIC) UC (BIV) Q Q Q Q Q Q 5Q 5Q 6Q 6Q Q Q Q Q Q Q 5Q 5Q 6Q 6Q EC-Tr EC-Po IMF OECD BP HP LIN Q Q Q Q Q Q 5Q 5Q 6Q 6Q Q Q Q Q Q Q 5Q 5Q 6Q 6Q Sources: European Commission, IMF, OECD and own calculaions. Noe: EC (P): deviaions from poenial (available only saring from ). EC (T): deviaions from Hodrick-Presco rend. Alhough capaciy uilisaion rae daa is no revised, revisions o real ime esimaes of deviaions of capaciy from average or rend relae o he fac ha he average and linear rend change as more daa are used o compue hem. In summary, five main resuls emerge from our analysis of real ime measures of he oupu gap in he euro area. Firs, here are subsanial changes in differen vinages of gap daa referred o he same quarer; someimes even he sign of he gap changes, and he size of he revision can be larger han he original value of he gap iself. Second, changes in he vinages of he ime series underlying he gap (e.g., real GDP) explain a minor par of he changes in 5

20 he gap. Third, changes in he vinages of he gap are mosly due o he recursive compuaion, which suggess eiher he need of a very long esimaion sample or, more likely, he presence of parameer changes. Fourh, averaging differen gap measures does no yield any subsanial gains. This finding is likely due o he raher high correlaion across alernaive gap measures. Finally, he UC based gap measures appear o be less subjec o revisions over ime. However, when confidence bands are compued for he UC based gaps, hey are fairly large, in paricular around urning poins, when precise measuremen would be need. This problem is jus hidden in he oher gap measures, for which confidence bands are eiher no available or no repored. IV. Uncerainy: A Comparison wih he US experience In his Secion we sudy he uncerainy characerising US oupu gap esimaes, also in comparison o he euro area. Afer a shor descripion of he US daa, we consider, in urn, he role of model uncerainy, parameer insabiliy, and daa uncerainy IV. Daa For he sake of clariy, in he case of he US we focus on he hree filer based esimaes of oupu gaps, namely, he HP filer ( HP ), he Baxer and King (999) band-pass filer ( BP ), and deviaions from a linear rend ( LIN ). The filers are compued using he same specificaion choices as for he euro area. Real GDP daa from he Federal Reserve Bank of Philadelphia s Real Time Daa Se for Macroeconomiss (RTDSM) is used. In order o consruc a complee se of quarerly vinages of quarerly esimaes, for hose vinages for which daa before 959 was no available (all hose of 99 and 996 as well as hose of 997Q and 999Q and Q), esimaes were exended backwards using (he changes in) he previously available hisorical vinage from he same source. Table 5 summarises he characerisics of he US oupu gap esimaes used in he paper. Overall, 66 vinages are available, depending on he se of esimaes. Appendix IV shows all vinages of all esimaes used. The availabiliy of so many vinages makes he analysis ineresing since we can also assess he effecs of he so-called Grea Moderaion wih a longer pos 985 sample, and evaluae wheher here have been any subsanial changes afer he exhausive analysis of Orphanides and van Norden () whose daa sop in 997. Table 5 Vinages of US oupu gap esimaes Daa and esimaes Definiion of rend Sample period Frequency Vinages Source Real GDP 97Q-6Q quarerly daa 965Q-7Q ( 66 ) RTDSM Band-pass filer Sochasic rend 985Q-6Q quarerly daa 965Q-7Q ( 66 ) own esimaes Hodrick-Presco filer Sochasic rend 985Q-6Q quarerly daa 965Q-7Q ( 66 ) own esimaes Linear rend filer Linear rend 985Q-6Q quarerly daa 965Q-7Q ( 66 ) own esimaes Source: RTDSM and own calculaions. Noes: Real GDP daa from he Federal Reserve Bank of Philadelphia s Real Time Daa Se for Macroeconomiss (RTDSM). 6

21 IV. Uncerainy measures IV... Model uncerainy In he absence of a well defined series of acual values, i is difficul o make an a priori choice on he bes esimaion mehod for he oupu gap. In addiion, alernaive mehods end o produce significanly differen esimaes of he gap, even wihin he same class of procedures. We have seen ha his is a relevan problem for he euro area, and we now evaluae wheher model uncerainy maer for filer-based gap esimaes for he US. Table 6 summarises he main feaures of he slack measures considered, wih reference o he final esimae, and Char 8 repors heir emporal evoluion. Several commens can be made. Firs, he pos 985 resuls are fairly differen from he full sample resuls. In paricular, and as expeced, he lower volailiy of GDP growh associaed wih he so-called Grea Moderaion is also refleced in lower volailiy of all he gap measures under consideraion. Second, he pos 985 resuls are fairly similar o hose for he euro area, in erms of boh volailiy and persisence of he gap measures. Third, he pos resuls indicae a furher reducion in volailiy and persisence of he gap measure. We will come back o his issue in he real ime evaluaion laer on. Finally, as for he euro area, he revisions in oupu gap esimaes end o be larger han hose in real GDP growh (see Char 9 and Appendix IV for more examples). Table 6 US oupu gap summary saisics mean s dev min max AR whole sample period (97-6) GDP growh Band-Pass Filer HP Filer Linear Filer Average Filers GDP growh Band-Pass Filer HP Filer Linear Filer Average Filers GDP growh Band-Pass Filer HP Filer Linear Filer Average Filers Noes: AR refers o he firs order auocorrelaion coefficien. 7

22 Char 8: Final esimaes of US oupu gap (percenage deviaions from rend/poenial oupu/average) 6 HP BP LIN Av-Fil Q 95Q 956Q 959Q 96Q 965Q 968Q 97Q 97Q 977Q 98Q 98Q 986Q 989Q 99Q 995Q 998Q Q Q 95Q 95Q 956Q 959Q 96Q 965Q 968Q 97Q 97Q 977Q 98Q 98Q 986Q 989Q 99Q 995Q 998Q Q Q Sources: RTDSM and own calculaions. Char 9: Vinages of US real GDP growh (percenages, year-on-year growh) Q 95Q 95Q 956Q 959Q 96Q 965Q 968Q 97Q 97Q 977Q 98Q 98Q 986Q 989Q 99Q 995Q 998Q Q Q Sources: RTDSM. 65Q 66Q 66Q 66Q 66Q 67Q 67Q 67Q 67Q 68Q 68Q 68Q 68Q 69Q 69Q 69Q 69Q 7Q 7Q 7Q 7Q 7Q 7Q 7Q 7Q 7Q 7Q 7Q 7Q 7Q 7Q 7Q 7Q 7Q 7Q 7Q 7Q 75Q 75Q 75Q 75Q 76Q 76Q 76Q 76Q 77Q 77Q 77Q 77Q 78Q 78Q 78Q 78Q 79Q 79Q 79Q 79Q 8Q 8Q 8Q 8Q 8Q 8Q 8Q 8Q 8Q 8Q 8Q 8Q 8Q 8Q 8Q 8Q 8Q 8Q 8Q 8Q 85Q 85Q 85Q 85Q 86Q 86Q 86Q 86Q 87Q 87Q 87Q 87Q 88Q 88Q 88Q 88Q 89Q 89Q 89Q 89Q 9Q 9Q 9Q 9Q 9Q 9Q 9Q 9Q 9Q 9Q 9Q 9Q 9Q 9Q 9Q 9Q 9Q 9Q 9Q 9Q 95Q 95Q 95Q 95Q 96Q 96Q 96Q 96Q 97Q 97Q 97Q 97Q 98Q 98Q 98Q 98Q 99Q 99Q 99Q 99Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q Q 5Q 5Q 5Q 5Q 6Q 6Q 6Q 6Q 7Q IV... Parameer insabiliy For he euro area, recursive compuaion of he gap measures (wih he final daa vinage) revealed a subsanial insabiliy in he resuls, wih very low correlaion beween he pseudo real ime and he final gap esimaes. To assess wheher his is he case also for he US, we have compued he filer based gaps recursively over he period -6, and Table 7 repors some summary saisics for he alernaive measures. I urns ou ha he correlaion beween he pseudo real ime esimaes and he final is much higher han for he euro area. Moreover, wih respec o he final vinage resuls, here is slighly more volailiy and persisence for he HP and BP based measures, less in he case of he linear filer based gap. These findings sugges ha also in he mos recen period recursive calculaion of he US gap is a source of changes in is magniude and someimes even in is sign, bu ha he problem is smaller compared o he euro area. 8

23 Table 7 Pseudo real ime esimaes of he US oupu gap mean s dev min max AR corr sign Band-Pass Filer Peudo RT % Rev FP HP Filer Peudo RT % Rev FP Linear Filer Peudo RT % Rev FP Noes: Sample period is : o 6: in all cases ( observaions). AR refers o he firs order auocorrelaion coefficien. Rev FP sands for revision final esimae minus (pseudo) real ime esimae. sign refers o he percenage of imes he pseudo real ime esimae has he same sign as he final esimae corr repors he correlaion beween pseudo real ime esimaes and final esimae in he Pseudo RT row and he correlaion beween pseudo real ime esimaes and he revision final esimae minus (pseudo) real ime in he Rev FP row. IV... Daa uncerainy We now compare he final esimaes wih fully real ime esimaes, compued recursively using in each quarer he available vinage of daa. To sar wih, we consider differences beween final and real ime (yearly) real GDP growh, which provides an indicaion of he exen of daa revisions in he GDP series ha underlies mos gap measures. We sress again ha in he paper final refers o he laes available vinage. From Table 8 (and Char 9), on average real GDP growh is slighly overesimaed in real ime, and he gap is less negaive when based on he BP or HP filers. I is also slighly more volaile and persisen han when compued wih he full sample of final daa. In addiion, he correlaions beween he real ime BP and HP esimaes and he revision error are much larger in absolue value han hose beween he final esimaes and he errors, which provides evidence in favour of he news hypohesis. Insead, for he euro area, boh corresponding correlaions were large, and he resuls no conclusive. 9

24 Table 8 Revisions o real ime US oupu gap esimaes mean s dev min max AR corr sign GDP Final RT % Rev RT Band-Pass Filer Final RT % Rev RT HP Filer Final RT % Rev RT Linear Filer Final RT % Rev RT Average Filers Final RT % Rev RT Noes: Sample period is : o 6: in all cases ( observaions). AR refers o he firs order auocorrelaion coefficien. Rev RT sands for revision final esimae minus real ime esimae. sign refers o he percenage of imes he real ime esimae has he same sign as he final esimae corr repors he correlaion beween real ime esimae and final esimae in he Final row, he correlaion beween real ime esimae and he revision (final minus real ime) in he RT row, and he correlaion beween final esimae and he revision (final minus real ime) in he Rev RT row. To disenangle he relaive role of recursive compuaion and real ime daa, we plo he oal revision error and he error purely due o daa revisions. Char presens resuls for he whole sample, which are useful for comparison wih Orphanides and van Norden () who use daa up o 997. From Char, i seems ha he oal revision error is slighly smaller afer, associaed wih a smaller daa revision componen. However, such a paern could change if he pos daa will be subjec o addiional revisions in fuure releases. Finally, a direc comparison of he revision process for he US and he euro area is provided in Chars and. I urns ou ha he overall average revision is smaller for he US, and ha he real ime gap esimaes follow more closely he final esimaes (a fac which underlies he higher correlaion in Table 8). However, he daa revision componen is larger in he US han in he euro area. In summary, his Secion shows ha real ime esimaes of he US oupu gap remain unreliable also in he mos recen period, even hough hey are more correlaed wih final values han for he euro area. In addiion, he daa revision componen of he revision error is larger han for he euro area.

25 Char : Real ime esimaes of US oupu gap, oal revision and daa revision (percenage poins) Band-pass filer esimaes RT esimaes oal revision daa revision Q 968Q 97Q 97Q 97Q 976Q 978Q 98Q 98Q 98Q 986Q 988Q 99Q 99Q 99Q 996Q 998Q Q Q Q 6Q HP filer esimaes RT esimaes oal revision daa revision Q 968Q 97Q 97Q 97Q 976Q 978Q 98Q 98Q 98Q 986Q 988Q 99Q 99Q 99Q 996Q 998Q Q Q Q 6Q Linear rend filer esimaes RT esimaes oal revision daa revision 966Q 968Q 97Q 97Q 97Q 976Q 978Q 98Q 98Q 98Q 986Q 988Q 99Q 99Q 99Q 996Q 998Q Q Q Q 6Q Sources: RTDSM and own calculaions.

26 Char : Real ime esimaes of he oupu gap, oal revision and daa revision ( onwards) (percenage poins) Euro Area US Band-pass filer esimaes RT esimaes oal revision daa revision RT esimaes oal revision daa revision Q Q Q Q Q Q 5Q 5Q 6Q 6Q Q Q Q Q Q Q 5Q 5Q 6Q 6Q HP filer esimaes RT esimaes oal revision daa revision RT esimaes oal revision daa revision Q Q Q Q Q Q 5Q 5Q 6Q 6Q Q Q Q Q Q Q 5Q 5Q 6Q 6Q Linear rend filer esimaes RT esimaes oal revision daa revision RT esimaes oal revision daa revision -6-6 Q Q Q Q Q Q 5Q 5Q 6Q 6Q Q Q Q Q Q Q 5Q 5Q 6Q 6Q Sources: Own calculaions.