WORKING PAPER NO. 276 SHORT-TERM ESTIMATES OF EURO AREA REAL GDP BY MEANS OF MONTHLY DATA GERHARD RÜNSTLER, FRANCK SÉDILLOT

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1 EUROPEAN CENTRAL BANK WORKING PAPER SERIES E C B E Z B E K T B C E E K P WORKING PAPER NO. 276 SHORT-TERM ESTIMATES OF EURO AREA REAL GDP BY MEANS OF MONTHLY DATA GERHARD RÜNSTLER, FRANCK SÉDILLOT SEPTEMBER 2003

2 EUROPEAN CENTRAL BANK WORKING PAPER SERIES WORKING PAPER NO. 276 SHORT-TERM ESTIMATES OF EURO AREA REAL GDP BY MEANS OF MONTHLY DATA 1 GERHARD RÜNSTLER 2, FRANCK SÉDILLOT 3 SEPTEMBER The paper was wrien while F. Sedillo was saff member of he Euro Area Macroeconomics Developmens Division a he ECB.We are especially graeful o M. Diron, S. Siviero, G. Parigi, an anonymous referee and he paricipans of he Eurosysem Working Group of Forecasing held in June 2002 for valuable commens on earlier versions of he paper. The opinions expressed in his paper are hose of he auhors and do no necessarily reflec he views of eiher he ECB or he OECD.This paper can be downloaded wihou charge from hp:// or from he Social Science Research Nework elecronic library a hp://ssrn.com/absrac_id= European Cenral Bank, Kaisersraße 29, D Frankfur, gerhard.ruensler@ecb.in 3 OECD, 2 rue André Pascal, F Paris Cedex 16, franck.sedillo@oecd.org

3 European Cenral Bank, 2003 Address Kaisersrasse 29 D Frankfur am Main Germany Posal address Posfach D Frankfur am Main Germany Telephone Inerne hp:// Fax Telex ecb d All righs reserved. Reproducion for educaional and non-commercial purposes is permied provided ha he source is acknowledged. The views expressed in his paper do no necessarily reflec hose of he European Cenral Bank. ISSN (prin) ISSN (online)

4 Table of Conens Absrac 4 Non echnical summary 5 1 Inroducion 6 2 The daa se 8 3 Quarerly bridge equaions for euro area gdp growh 9 4 Model selecion under complee monhly informaion The informaion conen of individual indicaors Combined bridge equaions and composie indicaors Ou-of-sample resuls 14 5 Ou-of-sample forecass under incomplee monhly informaion Forecasing monhly indicaors: ou-of-sample resuls GDP forecass under incomplee informaion: ou-of-sample resuls 19 6 Conclusions and remaining issues 21 References 31 Annex 25 European Cenral Bank working paper series 29 ECB Working Paper No 276 Sepember

5 Absrac The firs official daa releases of quarerly real GDP for he euro area are published abou eigh weeks afer he end of he reference quarers. Meanwhile, ongoing economic developmens mus be assessed from various, more readily available, monhly indicaors. We examine in he conex of univariae forecasing equaions o wha exen monhly indicaors provide useful informaion for predicing euro area real GDP growh over he curren and he nex quarer. In paricular, we invesigae he performance of he equaions under he case ha he monhly indicaors are only parially available wihin he quarer. For his purpose, we use ime series models o forecas he missing observaions of monhly indicaors. We hen examine GDP forecass under differen amouns of monhly informaion. We find ha already a limied amoun of monhly informaion improves he predicions for curren-quarer GDP growh o a considerable exen, compared wih ARIMA forecass. Equaions based on eiher quaniaive aciviy indicaors or he CEPR EuroCOIN composie indicaor perform bes. JEL classificaion: C22, C53 Key words: Conjuncural analysis, bridge equaions, incomplee monhly informaion 4 ECB Working Paper No 276 Sepember 2003

6 NON-TECHNICAL SUMMARY Firs official releases of quarerly naional accouns are published wih some delay. Eurosa publishes he firs official esimae of euro area real GDP abou 8 weeks afer he end of he respecive quarer. In order o assess he mos recen developmens in economic aciviy, economic forecasers hus pay high aenion o various monhly indicaors, which are more readily available. Examples of such indicaors include quaniaive aciviy indicaors (such as indusrial producion and reail rade daa), business surveys, financial variables and composie indicaors. A number of sudies have used univariae forecasing ( bridge ) equaions o obain shor-erm predicions of GDP from monhly indicaors. These sudies unambiguously conclude ha he monhly informaion improves he predicions of GDP growh o a considerable exen. The majoriy of hese sudies, however, do no provide paricularly imely predicions, because hey are based on quarerly aggregaes of monhly indicaors and herefore require ha he indicaors are known for he enire quarer. For he euro area, he complee se of indicaors is available only wo weeks in advance of he firs official release of real GDP. Hence, using bridge equaions under full monhly informaion adds very lile o he imeliness of conjuncural analysis. In his paper we herefore invesigae he forecasing performance of he equaions under he case ha he monhly indicaors are only parially available wihin he quarer. For his purpose, we combine he quarerly bridge equaions for GDP growh wih monhly ime series models o forecas he missing observaions of monhly indicaors. This approach allows us o obain predicions for GDP growh based on incomplee monhly informaion. We find ha bridge equaions based on eiher quaniaive indicaors or he CEPR EuroCOIN indicaor provide useful informaion for assessing he curren sae of he euro area economy, even when based on a limied coverage of monhly daa. GDP forecass for he curren quarer improve subsanially upon forecass from sandard ime series model for GDP. This improvemen also exends o forecass for nex-quarer GDP growh. ECB Working Paper No 276 Sepember

7 1 INTRODUCTION Firs official releases of quarerly naional accouns are published wih some delay. Eurosa publishes he firs official esimae of euro area real GDP abou 8 weeks afer he end of he respecive quarer. 4 For economic policy purposes, his delay sands in quie some conras o he need for imely and reliable informaion on he sae of he economy. For insance, such informaion is essenial as a saring poin for macroeconomic forecass. 5 In order o assess he mos recen developmens in economic aciviy, economic forecasers and marke paricipans hus pay high aenion o conjuncural informaion from indicaors, which are available more promply a monhly frequency. Examples of such indicaors include quaniaive aciviy indicaors (such as indusrial producion and reail rade daa), business surveys, financial variables and composie indicaors. Usually, his informaion is used in a purely qualiaive manner. A number of aemps have ye been made o invesigae he benefis of incorporaing monhly indicaors ino saisical forecasing models. Sudies unambiguously conclude ha his resuls in considerable improvemens in predicions of curren-quarer GDP growh. There is also some evidence ha he improvemen exends beyond he curren quarer, alhough he gains decrease very fas wih he projecion horizon. Typically, sudies use univariae forecasing ( bridge ) equaions o obain shor-erm predicions of GDP and oher naional accoun aggregaes from monhly indicaors. Such mehodology has been implemened for US daa (Trehan, 1992; Ingenio and Trehan, 1996) and, o lesser exen, for individual euro area counries, as e.g. by Parigi and Schlizer (1995) and Bovi e al. (2000) for Ialy, Irac and Sédillo (2002) for France and Camba-Mendez e al. (2001), Mourougane and Roma (2002) and van Rooij and Sokman (2001) for various European counries. Baffigi e al. (2002) and Grasmann and Keereman (2002) have underaken wo recen sudies for aggregae euro area daa. Several sudies have also examined he benefis of including monhly daa ino quarerly simulaneous equaion models (e.g. Corrado and Green, 1988; Miller and Chin, 1996; Sark, 2000). The majoriy of hese sudies, however, do no provide paricularly imely predicions of GDP growh, because hey are based on quarerly aggregaes of monhly indicaors and herefore require ha he indicaors are known for he enire quarer. For he euro area, he complee se of indicaors is available only wo weeks in advance of he firs official release of real GDP. Hence, using bridge equaions under full monhly informaion in fac adds very lile o he imeliness of conjuncural analysis. Several sudies (Reynaud and Sherrer, 1996; Camba-Mendez e al., 2001) have aemped o overcome 4 Since he 1 s quarer of 2003, Eurosa also publishes a flash esimae wih a delay of 6 weeks. This esimae is based on a limied se of daa releases from official naional sources, while he daa for he remaining counries are prediced from various sources (Eurosa, 2003). 5 For example, mos inernaional and European insiuions publish Spring macroeconomic forecass for he euro area in April or May. Such forecass have no official esimaes for euro area GDP in he 1 s quarer of he respecive year available and herefore mus rely on monhly informaion. The same applies o he Eurosysem saff Spring projecions, which are published in he June issue of he ECB Monhly Bullein. The Eurosa flash esimae becomes available a a lae sage of he Eurosysem exercise. 6 ECB Working Paper No 276 Sepember 2003

8 his difficuly by forecasing quarerly aggregaes of monhly indicaors from VAR models. Sudies, which deal wih he efficien reamen of new monhly informaion ha becomes available wihin he quarer are ye scarce and are limied o US daa (Rahjens and Robins, 1993; Ingenio and Trehan, 1996; Roberson and Tallman, 1999). In his paper we invesigae he forecasing performance of he equaions under he case ha he monhly indicaors are only parially available wihin he quarer. For his purpose, we combine quarerly univariae bridge equaions o predic GDP growh wih monhly ime series models o forecas he missing observaions of monhly indicaors. This approach allows us o obain predicions for GDP growh based on incomplee monhly informaion. We hereby aemp o rea in an efficien manner he saggered iming of monhly daa releases and o obain rolling predicions for GDP growh based on he mos recen se of monhly informaion. The srucure of he paper is as follows. Afer presening he daa se in secion 2, we se ou he bridge equaion in secion 3 and discuss our model selecion sraegy. We also show he iming of monhly daa releases and implemen an updaing scheme, which reflecs he publicaion schedule of he paricular indicaors wihin he quarer. The empirical analysis proceeds in wo seps. Secion 4 sars wih he assumpion ha he monhly indicaors are known for all hree monhs wihin he curren quarer. We use sandard model selecion procedures o derive various versions of bridge equaions. Secion 5 hen examines he forecasing properies of he equaions for he case of incomplee monhly informaion. Based on he publicaion scheme of monhly daa, we inspec GDP forecass under differen amouns of monhly informaion. We invesigae various mehods o forecas he missing values of monhly indicaors including univariae ARIMA models, a Bayesian VAR (Doan e al., 1984) and mulivariae srucural ime series models (Harvey and Koopman, 1997). To anicipae our main findings, bridge equaions based on eiher quaniaive indicaors or composie indicaors (noably he CEPR EuroCOIN indicaor) provide useful informaion for assessing he curren sae of he euro area economy, even when based on a limied coverage of monhly daa. GDP forecass for he curren quarer improve subsanially upon forecass from a univariae ARIMA model for GDP, wih he roo mean squared error being nearly halved. Once missing observaions of monhly indicaors are forecas from mulivariae models, his improvemen also exends o GDP predicions for he nex quarer. Secion 6 concludes and proposes some avenues for furher work. The presen sudy suffers from wo caveas relaed o daa limiaions. Firs, due o a lack of hisorical real-ime daa, he esimaes are based on final daa releases. Second, he daa used in he sudy are derived from he aggregaion of naional sources, which are subjec o differen seasonal adjusmen mehods. Given he noisy characer of some of he daa and he subsequen revisions o iniial daa releases, hese wo feaures may have non-negligible impacs on he findings. A comparison wih he resuls of a disaggregaed approach, which is based on real-ime daa and counry-specific equaions, may herefore be of ineres. ECB Working Paper No 276 Sepember

9 2 THE DATA SET The daa se ranges from 1990 Q1 o 2001 Q4 and comprises available euro area indicaors and composie indicaors ogeher wih some recompued indicaors based on various sources. The se of quaniaive real aciviy indicaors ha are available for he euro area is quie limied. We use indusrial producion excluding consrucion (IP), new car regisraions (CR), a reail sales indicaor (RS) and an indicaor of indusrial producion in consrucion (IPC). The daa are used in logs. Daa on IP are published by Eurosa, whereas daa from CR are released by ACEA. RS and IPC are consruced from available counry informaion. The RS indicaor comprises Duch, German and Spanish reail rade daa (excluding car sales) and French consumpion in manufacured goods excluding cars. The indicaor is calculaed as a weighed average of hese daa based on consumpion weighs. Sédillo (2002) repors ha he indicaor provides raher accurae early esimaes of consumpion growh in he euro area. The IPC indicaor is calculaed as a weighed average of German and French daa, based on GDP weighs. The limied counry coverage of he laer wo indicaors is due o a lack of imely available daa for he remaining euro area counries. Among business surveys daa, we use he main indices from he European Commission surveys (Commission, 2001), i.e. he business climae index (BCI) and he consumer confidence index (CCI). In addiion, we compue a reail climae index (RCI) as he firs principal componen of he four balances of opinions included in he Commission reail rade survey. Among available composie indicaors, we use he overall Commission s economic senimen index (TSEN), he CEPR EuroCOIN (ECN) indicaor (Forni e al., 2001) and he de-rended OECD (2002) leading indicaor (OLI). These indicaors are readily available and widely recognised. The OECD leading indicaor is inended o predic cyclical movemens in indusrial producion. The euro area aggregae is calculaed from an aggregaion of naional indicaors. The laer have been consruced in a similar fashion and usually comprise survey daa, financial variables (ineres rae spreads and sock indexes), he erms of rade, and new passenger car regisraions. The EuroCOIN indicaor, developed by he CEPR and he Banca d Ialia, is consruced from a dynamic facor analysis of an exensive number of monhly indicaors from euro area naional sources. I is inended o rack he principal common facor in euro area economic aciviy. Finally, we compue wo composie indices from he above real aciviy indicaors and business survey daa. Composie index PCI1 comprises he available monhly real aciviy daa (IP, IPC, CR, and RS), whereas indicaor PCI2 also comprises he above lised business survey daa. Following he US Conference Board (2000) composie index, he wo indices are formed as he weighed sum of monh-on-monh changes of he paricular indicaors wih he weighs being given as he inverse of he sandard deviaions of firs differences. 8 ECB Working Paper No 276 Sepember 2003

10 3 QUARTERLY BRIDGE EQUATIONS FOR EURO AREA GDP GROWTH To predic quarerly real GDP growh from he above monhly indicaors, we aggregae he laer o quarerly frequency and use he Auoregressive Disribued Lag (ADL(p,q)) equaion y denoes he log of real GDP and where operaor, while / and k ρ L) y = δ ( L) x + ε ( (1) j=1 j j j, x, denoe monhly indicaors. denoes he difference j(l) denoe lag polynomials of order p and q j, respecively. Since indicaors x j, are published in advance of he firs esimae of GDP, equaion (1) can be used o obain predicions of he laer from daa of he indicaors for he same quarer. As noed in he inroducion, we will pu special emphasis on he case of monhly indicaors being only parially observed wihin he quarer. However, we do no inend o develop forecasing equaions, which are specific o he available monhly informaion. Such approach would resul in revisions o he predicions for GDP growh, which parially reflec differen specificaions of he forecasing equaions, and hereby in applicaion blur he informaion conained in new monhly informaion. The analysis of he sources of revisions o earlier predicions is ye an imporan elemen in applicaion. In addiion, he raher shor sample ha we have available calls for a robus approach o model selecion. In he case of incomplee monhly informaion, in urn, missing observaions of monhly indicaors mus be forecas o obain he quarerly aggregaes, which ener equaion (1). Clearly, in his case, he GDP predicions hen also depend on he properies of he forecass of monhly indicaors. Our analysis will herefore proceed in wo seps. Secion 4 sars wih he assumpion ha he monhly indicaors are known for all hree monhs wihin he curren quarer. Based on in-sample model selecion crieria, we will derive various versions of bridge equaion (1). In a second sep, secion 5 hen examines he ou-of-sample forecasing properies of he paricular equaions under differen ses of monhly informaion. We will use a number of mehods o forecas he missing daa on monhly indicaors. Overall, his shall give an indicaion of he robusness of he findings from sep 1 wih respec o incomplee monhly informaion. In applicaion, he forecass under incomplee monhly informaion are dicaed by he iming of monhly daa releases. Generally, he indicaors discussed in secion 2 are published wih a delay of abou wo monhs wih he excepion of business survey daa and CR, which are published wih a delay of abou one monh. Daa for indusrial producion (IP) are published las among he indicaors under consideraion. To undersand how he sequence of forecass works in pracice, le us examine he example of daa releases in early 2002, as shown in Figure 1. A firs esimae of real GDP in 2002 Q1 was published on 30 May On 19 June 2002, afer he release of IP daa, all indicaors were available for April 2002, i.e. he firs monh of 2002 Q2 (while business surveys and CR were already available for May). ECB Working Paper No 276 Sepember

11 We ake his as he saring poin o produce he firs forecas for GDP in 2002 Q3 and denoe his as he 1 s nex-quarer forecas. A he same ime, we compue he 1 s curren-quarer forecas for 2002 Q2. The wo forecass rely on one monh of informaion for 2002 Q2 (and wo monhs for business surveys daa and CR). Hence, forecass for monhly indicaors mus be produced for periods of up o wo and five monhs ahead, for curren and nex-quarer forecass, respecively. On 19 July 2002, he se of monhly informaion is exended by one monh and we compue he 2 nd nex-quarer forecas for 2002 Q3 and he 2 nd curren-quarer forecas for 2002 Q2. On 19 Augus 2002 hen all monhly daa for 2002 Q2 are known. This consiues he dae for he 3 rd se of forecass for 2002 Q2 and 2002 Q3, respecively. Going furher ahead, on 30 Augus Eurosa released is firs esimae for real GDP for 2002 Q2. Thus he forecass would no longer cover 2002 Q2 and he updaing scheme is shifed one quarer forward. On 19 Sepember 2002, afer he release of IP for July 2002, he 1 s curren-quarer forecas for 2002 Q3 would be compued, ogeher wih he 1 s nex-quarer forecas for 2002 Q4. Figure 1: Monhly updaing scheme of daa releases Real GDP Q4 Q1 Firs official esimae 2002Q2 2002Q1 (1s (4h curr. es.) quarer fcs.) 2002Q3 2002Q2 (1s (1s nex es.) quarer fcs.) 2002Q2 2002Q1 (2nd(5h curr. es.) quarer fcs.) 2002Q3 2002Q2 (2nd (2nd nex es.) quarer fcs.) 2002Q2 2002Q1 (3rd(6h curr. es.) quarer fcs.) 2002Q3 2002Q2 (3rd (3rd nex es.) quarer fcs.) 730 March May March June April July Augus May 2002 Indicaors: IP, RS: 1m 1m daa daa, released, 5m fcs 5m fcs (Surveys Oher and vars: CR: 2m 2m daa, daa, 4m 4m fcs fcs) Indicaors: IP, 2m RS: daa 2m released, daa, 4m fcs 4m fcs (Surveys Oher and vars: CR: 3m daa, 3m fcs) Indicaors: IP, RS: 3m daa, released, 3m fcs 3m fcs (Surveys Oher vars: and 4m CR: daa, 4m daa, 2m fcs 2m fcs) Overall, a sequence of six forecass for quarerly GDP growh in a given quarer is produced, based on differen ses of monhly informaion. The firs hree (nex-quarer) forecass are solely based on monhly informaion from he previous quarer (whereas previous-quarer GDP growh is no ye known). The subsequen curren-quarer forecass, in urn, are based on a parial se of wihin-quarer informaion of monhly indicaors (and previous quarer GDP growh is already known). In paricular, he final (3 rd ) curren quarer is based on complee monhly informaion. This forecas is conduced abou wo weeks in advance of he firs official release of GDP. 4 MODEL SELECTION UNDER COMPLETE MONTHLY INFORMATION We sar our empirical analysis under he assumpion ha monhly indicaors are known for all hree monhs wihin he quarer. Afer inspecion of he forecasing properies of he individual indicaors in secion 4.1, we will form combined bridge equaions in secion 4.2 by means of sepwise regressions. We will furher compare he laer wih bridge equaions based on he composie indicaors. 10 ECB Working Paper No 276 Sepember 2003

12 4.1 The informaion conen of individual indicaors As a firs sep, and in order o obain preliminary insighs ino he informaion conen of individual indicaors, we follow Blake e al. (2000) and esimae equaion (1) for he individual indicaors inroduced in secion 2. We resric he analysis o real aciviy indicaors and business survey daa and will urn o he composie indicaors laer on. Table 1 repors he sum of squared residuals (SSR), he roo mean squared errors (RMSE) of GDP predicions for he curren quarer and F-ess for he significance of he indicaors (i.e. agains he hypohesis of δ ( L) = 0 ). Quaniaive indicaors are used in firs differences, whereas survey daa ener he equaions in levels. 6 j Table 1 Predicive capabiliy of individual euro area indicaors (Sample period: 1990 Q2 o 2001 Q4) SSR (*100) RMSE (*100) F Tes ( L) = 0 δ j P val Encompassing regression Quaniaive indicaors Indusrial producion IP (0.00) Car regisraions CR (0.00).78 (.12) Reail sales indicaor RS (0.00).79 (.12) Indusrial prod. consrucion IPC (0.15).94 (.13) Business surveys Business climae BCI (0.00) 1.15 (.18) Consumer confidence CCI (0.00) 1.07 (.16) Reail rade climae RCI (0.02) 1.04 (.16) All indicaors, wih he excepion of IPC, are significan. Indusrial producion excl. consrucion (IP) is ye far ahead of he oher series in erms of predicive conen. The RMSE of GDP predicions from IP amouns o 0.28 pp, compared wih RMSEs in a range of 0.38 o 0.47 pp for he oher variables. Given he superior performance of IP, i is of ineres o see wheher he remaining indicaors add informaion o he GDP predicions based on IP. We herefore run he encompassing regressions y = λyˆ ( IP) + (1 λ) yˆ ( j) where ( ) ˆ IP y and ( ) yˆ j denoe GDP predicions from IP and he alernaive indicaor, respecively. The esimaes of λ are repored in Table 1 ogeher wih heir sandard errors. A value of of lower han one implies ha he alernaive indicaor adds informaion o GDP predicions from IP. Indicaors CR and RS appear o conain some addiional informaion o IP wih being significanly smaller han one in boh cases. In conras, and quie ineresingly, λ is esimaed o be larger han one for business 6 Diebold and Kilian (2000) argue ha differencing in order o render he series saionary, according o uni roo pre-esing, improves he forecasing performance. Uni roo ess largely confirm he convenional wisdom abou he saionariy properies of he individual indicaors, i.e. nonsaionariy of quaniaive indicaors and saionariy of survey daa. For GDP, ess do no rejec he presence of a uni roo. The augmened Dickey- Fuller saisics (wih 4 lag) is -2.07, while he Phillips-Perron saisics (wih a runcaion lag of 3) gives 1.60, below he 5% criical values. ECB Working Paper No 276 Sepember

13 surveys indicaors BCI, CCI and RCI. Hence, he laer do no add informaion o IP for predicing curren-quarer GDP growh. 4.2 Combined bridge equaions and composie indicaors In his secion, we combine he individual indicaors o obain various versions of equaion (1) and examine he predicive conen of he composie indicaors and indices inroduced in secion 2. Overall, we invesigae eigh models, which may be grouped as follows. ΠModel AR is a univariae auoregressive model for GDP and is used as a benchmark; ΠEquaions SW1 and SW2 are derived from sepwise regressions of he indicaors shown in Table 1. We used he significance of F-ess (a he 5% level) as he crierion for inclusion of an indicaor. This crierion seleced he four indicaors IP, CR, IPC and RS. Equaion SW1 represens an inermediae sep of he sepwise regressions. This equaion conains IP and CR. Equaion SW2 conains he four indicaors IP, CR, IPC and RS. The purpose of mainaining he inermediae sep SW1 is o examine he robusness of he findings from he sepwise regressions agains ou-ofsample forecasing performance and, laer on, agains forecass based on incomplee informaion ses. ΠModels TSEN, ECN, OLI, PCI1 and PCI2 are based on he respecive composie indicaors and composie indices as described in secion 2. The indicaors are saionary by consrucion and, hence, ener equaion (1) in levels. The deailed specificaions of he equaions are described in Annex A. All equaions include wo dummies in 1992 Q1 and 1992 Q2 o accoun for sharp residual ouliers. In he equaions no including CR, a furher dummy is added for 1993 Q1. 7 The main resuls for hese equaions are repored in Table 2, along wih various diagnosic ess. Figures A.1 o A.7 in Annex A show he fied values of he equaions. Residual mis-specificaion ess indicae ha he equaions are well specified. In paricular, he resuls of he Chow predicive failure es sugges ha he equaions are fairly sable. The goodness-of-fi saisics of he bes-performing bridge equaions improve sharply upon he benchmark AR. The RMSE of he bes-performing models improves by some 50% o 60% on he benchmark AR. Model SW2 performs bes followed by model PCI1. The roo mean squared errors (RSMEs) of residuals from hese equaions amoun o 0.14 pp and 0.17 pp, respecively, compared o 0.31 pp for he benchmark AR and a sandard deviaion of GDP growh of 0.46 pp over he sample. Model ECN falls somewha shor of models SW2 and PC1, whereas he improvemen of models TSEN and OLI on he AR is quie limied. 7 These unusually large flucuaions in euro area GDP growh are largely accouned for by Germany. 12 ECB Working Paper No 276 Sepember 2003

14 Table 2 Summary saisics of he seven bridge equaions for euro area (Sample period: 1990 Q2 o 2001 Q4) Main saisics AR SW1 SW2 TSEN PCI1 PCI2 ECN OLI Adjused R RMSE (in pp) Diagnosic ess Durbin Wason LM (1) 0.62 (0.44) LM (4) 1.21 (0.32) ARCH(1) 1.37 (0.25) WHITE 0.37 (0.77) Normaliy 1.59 (0.45) RESET(2) 0.85 (0.43) CHOW (1) 0.49 (0.93) (0.97) 0.47 (0.75) 0.05 (0.83) 0.78 (0.61) 0.36 (0.84) 1.06 (0.36) 0.64 (0.82) (1) Predicive failure es over he period (0.59) 0.18 (0.95) 0.11 (0.74) 0.40 (0.95) 3.87 (0.14) 0.03 (0.97) 0.93 (0.55) 0.01 (0.94) 0.31 (0.86) 0.28 (0.60) 1.33 (0.26) 3.10 (0.21) 0.75 (0.48) 0.63 (0.83) 0.39 (0.53) 0.36 (0.83) 0.46 (0.50) 0.39 (0.81) 0.50 (0.78) 1.03 (0.36) 0.93 (0.55) 0.15 (0.70) 0.19 (94) 0.52 (0.48) 0.85 (0.57) 0.40 (0.82) 2.40 (0.11) 0.34 (0.98) 1.87 (0.18) 0.96 (0.44) 0.01 (0.93) 1.30 (0.27) 1.34 (0.51) 1.38 (0.26) 0.48 (0.93) 0.16 (0.68) 0.14 (0.96) 0.49 (0.49) 1.05 (0.41) 0.87 (0.65) 1.76 (0.18) 0.66 (0.80) Despie he sharp improvemen on he benchmark, he RMSE of 0.14 from model SW1 sill implies forecas confidence bounds of considerable size. The 90% confidence bound, for insance, amouns o ± 0.23 percenage poin. Hence, a forecas of, say, 0.30% for GDP growh would give rise o 90% upper and lower forecas confidence bounds of 0.07 o 0.53 pp, respecively, wih obviously very differen implicaions for conjuncural analysis. On he oher hand, Figures A.1 o A.7 show he beerperforming models o rack urning poins in GDP growh relaively closely. Various feaures of he resuls deserve some discussion. Firs, indicaors IP, CR, IPC and RS, which have been seleced from he sepwise regressions, happen o correspond exacly o he se of quaniaive real aciviy indicaors. This resul parallels hose repored in Table 1 and is also in line wih he findings of various relaed sudies for he US. The quaniaive indicaors are generally used by naional saisical agencies in he compilaion of quarerly naional accouns. Indusrial producion, in paricular, no only accouns for abou one hird of real GDP, bu is also among is more volaile componens. Is high predicive conen is herefore a direc oucome of is high imporance in producing naional accouns daa. Similar consideraions apply o CR and RS. ECB Working Paper No 276 Sepember

15 Second, he direc saisical link of quaniaive indicaors wih naional accouns perhaps also explains why he quaniaive indicaors wipe ou business survey daa. This should however no be aken as indicaion ha he laer are generally of limied relevance. For insance, he survey daa may be more useful when i comes o signalling urning poins in he business cycle (e.g., Baffigi e al., 2003). Third, he predicive performance of model PCI1 comes close o he one of SW2 and he ex-ane aggregaion of quaniaive indicaors does no considerably worsen he resuls. Again, he inclusion of survey daa ye worsens he performance of he composie index, as from he higher RMSE from equaion PCI2 compared o PCI1. Fourh, he above findings indicae ha a selecion procedure based on he informaion conen of he individual indicaors, as used e.g. by Blake e al. (2000), can give sub-opimal resuls, noably when indicaors are highly correlaed. Blake e al. (2000) form composie indices as weighed averages of he individual indicaors, wih he weighs deermined from he predicive conen of he individual indicaors, as from he RMSE repored in Table 1. The Blake e al. (2000) procedure would have implied, for insance, o aach a larger weigh o he BCI han o CR and RS (see Table 1). However, from he sepwise regressions, BCI does no add o he forecasing performance, whereas he inclusion of RS and CR improve he goodness of fi o a considerable exen. The reason is ha IP and BCI are highly correlaed and IP encompasses he BCI, bu no CR and RS. While a purely saisical approach would have suggesed o combine he indicaors of Table 1 also wih he composie indicaors from sepwise regressions, we did no aemp o do so. The reason is ha he composie indicaors are largely based on he same indicaors as we have examined in he sepwise regressions. One purpose of inspecing he composie indicaors is o learn abou he poenial gains from daa reducion echniques agains sepwise regressions. Combining individual and composie indicaors would have blurred his inenion. I has been argued ha, in view of he subsanial noise componen in monhly real aciviy indicaors, daa reducion echniques migh resul in improved forecasing performance. 4.3 Ou-of-sample resuls We urn o he ou-of-sample forecasing performance of he various equaions based on recursive parameer esimaes. 8 For now, we mainain he assumpion ha monhly indicaors are observed for all hree monhs of he respecive quarer. We follow a rule of humb in using one hird of he available sample for conducing he ou-of-sample forecass. This leaves an ou-of-sample period from 1998 Q1 o 2001 Q4. Table 3 repors he roo mean squared errors (RMSEs) of he recursive ou-of-sample forecass ogeher wih hose of he in-sample forecass, which were already repored in Table 2. Furher, Table 3 shows 8 This is, a each poin in ime he equaions are esimaed from he daa, which are available prior o he predicion period. To obain he GDP predicion for period, equaion (1) is esimaed from daa up o period ECB Working Paper No 276 Sepember 2003

16 he raios of he RMSEs of forecass from he various equaions agains he benchmark AR model and he bes performing model, SW2. Table 3 Recursive ou-of-sample forecass (1998 Q1 o 2001 Q4) AR SW1 SW2 TSEN PCI1 PCI2 ECN OLI RMSE ( in pp) Raio o AR 1.00 ***.58 ***.45 *.84 ***.54 ***.61 *** Raio o SW2 *** 2.21 * *** ** 1.35 ** 1.35 *** 1.93 * HLN es significan a 10% level; ** a he 5% level; *** a he 1% level. The RMSEs of ou-of-sample forecass urn ou o be very close o hose of in-sample forecass, alhough hey are in some cases slighly higher. This confirms he sabiliy of he equaions. In addiion, he relaive performances of he paricular equaions remain broadly unchanged compared wih he insample resuls, alhough he relaive performances of PCI2 and ECN improve somewha for ou-ofsample forecass. Table 3 also shows he resuls from Diebold-Mariano (1995) ess for he significance of he differences beween RMSEs. As discussed by Clark (1999), he finie sample behaviour of he es suffers from some size disorions. We hus use he Harvey, Leybourne and Newbold (HLN, 1997) modificaion of he es o correc for small sample disorions. We find ha forecass from SW2 improve upon he remaining models a he 10% significance level wih he excepion of PCI1, for which he significance value is slighly above 10%. Compared wih he benchmark AR model, all bridge equaions provide an improved forecas accuracy a he 1% hreshold wih he excepion of models OLI and TSEN. 5 OUT-OF-SAMPLE FORECASTS UNDER INCOMPLETE MONTHLY INFORMATION We now urn o he forecasing properies of he above bridge equaions under incomplee monhly informaion. Clearly, in such case he properies of he resuling predicions for GDP depend no only on equaion (1), bu also on he properies of he models o predic he missing monhly daa. The siuaion is complicaed by he fac ha monhly indicaors are published wih differen delays. Hence, he relaive forecasing performance of differen versions of equaion (1) may depend on he amoun of available monhly informaion and he opimal se of indicaors may vary. To examine hese issues, we conduc an ou-of-sample forecasing exercise along he lines of he updaing scheme described in secion 3. We produce rolling forecass for boh curren and nex-quarer GDP growh based on differen amouns of monhly informaion as from he updaing scheme. Secion 5.1 derives forecass for he missing monhly daa from various univariae and mulivariae ime series models. In secion 5.2, we hen inser he resuling forecass for quarerly aggregaes of ECB Working Paper No 276 Sepember

17 monhly indicaors ino he various bridge equaions and invesigae he forecasing performance of he laer under incomplee monhly informaion. To simplify he exercise, we limi his exercise o models o SW1, SW2, PCI1, ECN and OLI. 5.1 Forecasing monhly indicaors: ou-of-sample resuls We examine six models o generae forecass for monhly indicaors. As a benchmark, we employ a simple naïve projecion, which consiss of assuming a consan level a he las known value for he monhly indicaors. We furher use wo univariae ime series models, i.e. ARIMA and srucural ime series (STS) models (Harvey, 1989). The laer is designed o decompose a series ino a rend and an irregular componen (see Annex B). As regards ARIMA models, lag lengh selecion was based on he Schwarz informaion crierion (SIC). In addiion, we esimae hree mulivariae models, i.e. a VAR, a Bayesian VAR, and a mulivariae STS model. These models include indicaors BCI, IP, RS, CR, ECN and OLI. Lag lengh selecion in he VAR and he BVAR was based on he SIC. The BVAR model was se up wih a sandard Minnesoa prior as proposed by Doan e al (1984). The mulivariae STSM has been proposed by Harvey and Koopman (1997). The STS and BVAR models are discussed in more deail in Annex B. 9 Their usage is moivaed from earlier findings on heir poenially beer forecasing performance compared o he ARIMA and VAR models (Doan e al. 1984; Rick, 1994). We did no invesigae error correcions (VEC) models. As poined ou by Hoffman and Rashe (1996), forecass from VEC models do no necessarily improve upon VAR models over shor forecas horizons. Conrary o Rahjens and Robins (1993), we have preferred o specify he forecasing equaions direcly in erms of monhly daa, and o aggregae he predicions o quarerly frequency hereafer. This enables us o easily carry ou muli-sep ahead projecions. Rahjens and Robins (1993) use quarerly aggregaes of monhly indicaors, bu include informaion on he wihin-quarer dynamics of he indicaors by defining a furher variable as he difference beween he hird monh of he quarer and he average of he quarer. However, his approach precludes any muli-sep ahead projecions, unless an auxiliary equaion is used o predic he addiional variable. Indeed, Rahjens and Robins (1993) do no find any improvemens in muli-sep ahead forecass from he inclusion of he wihin-quarer variable. In he mulivariae models, we aemp o make efficien use of he available informaion se. As noed in secion 3, BCI and CR are known one monh in advance of oher indicaors. We use sandard procedures o condiion he one-sep ahead forecass for IP, RS, OLI and ECN on he addiional 9 The predicions for composie indicaor PCI1 are derived from he forecass of he individual indicaors. 16 ECB Working Paper No 276 Sepember 2003

18 observaions for CR and BCI. As regards VAR and BVAR forecass, we use condiional forecass as proposed by Doan e al. (1984), generaed from a block riangular facorisaion of he residual covariance marix. In he mulivariae STSM, condiioning is simply performed by he Kalman filer (see Harvey, 1989:463f). Using such condiional forecass resuled in some, albei small improvemens in forecass for IP. The models were recursively esimaed over he period of 1998:1 o 2001:12. Table 4 repors he RMSEs of he recursive forecass for he quarer-on-quarer growh raes of seleced indicaors. The numbering of he forecass in Table 4 refers o he updaing scheme for GDP predicions, as described in secion 3. For insance, he 3 rd curren-quarer forecas is rivial, as monhly indicaors are available over he enire quarer and he RMSE is, hence, idenical o zero. For CR and BCI, which are published one monh earlier, he same applies already o he 2 nd curren-quarer forecas. Table 4 Quarer-on-quarer growh rae of seleced indicaors (Ou-of-sample RMSE from 1998 Q1 o 2001 Q4) Model for projecing monhly indicaors Univariae models Mulivariae models Wihin quarer informaion Naïve ARIMA STS MSTS VAR BVAR Indusrial producion (1.110) Nex quarer 1 s forecas nd forecas rd forecas Curren quarer 1 s forecas nd forecas rd forecas Reail sales indicaor (0.701) Nex quarer 1 s forecas nd forecas rd forecas Curren quarer 1 s forecas nd forecas rd forecas Car regisraions (2.821) Nex quarer 1 s forecas nd forecas rd forecas Curren quarer 1 s forecas nd forecas rd forecas Noe: The numbers in brackes in he firs column show he sandard deviaions of quarerly growh raes of he indicaors hrough 1998 Q Q4. Overall, for curren-quarer predicions, he improvemen in forecas accuracy from he various models upon he naïve forecas is raher limied, alhough some improvemen occurs for he 1 s forecas, which ECB Working Paper No 276 Sepember

19 uses one monh of observaions wihin he quarer. As regards he nex-quarer forecass, however, mulivariae models provide somewha beer forecass for mos indicaors. This holds in paricular for IP and composie indicaor PCI1, as OLI and, o a lesser exen BCI and ECN, appear o conain imporan predicive conen for IP. Overall, he BVAR appears o perform bes. For CR and RS, in urn, none of he mehods performs well and he bes univariae model ouperforms he mulivariae mehods. Table 4 (cond.) Quarer-on-quarer growh rae of seleced indicaors (Ou-of-sample RMSE from 1998 Q1 o 2001 Q4) Model for projecing monhly indicaors Univariae models Mulivariae models Naïve ARIMA STS MSTS VAR BVAR Composie indicaor PCI1 (0.660) Nex quarer 1 s forecas nd forecas rd forecas Curren quarer 1 s forecas nd forecas rd forecas ECN (level) (0.194) Nex quarer 1 s forecas nd forecas rd forecas Curren quarer 1 s forecas nd forecas rd forecas OLI (1.107) Nex quarer 1 s forecas nd forecas rd forecas Curren quarer 1 s forecas nd forecas rd forecas Noe: The numbers in brackes in he firs column show he sandard deviaions of he indicaors hrough 1998 Q Q4. Generally, knowledge of one monh of informaion already subsanially reduces he RMSE of he predicions. This also holds for he naïve forecas. As regards indusrial producion for insance, he RMSE of he forecas based on daa for he previous quarer only (i.e. he 3 rd nex-quarer forecas) amouns o 1.12 pp. Adding one monh of daa for he curren quarer (he 1 s curren-quarer forecas) more han halves he RMSE o 0.54 pp. Two monhs of informaion reduce he RMSE of he naïve forecas furher o 0.23 pp. These improvemens are a direc resul of he aggregaion properies of 18 ECB Working Paper No 276 Sepember 2003

20 growh raes. As discussed in Annex B, quarer-on-quarer growh raes can be approximaed from a weighed average of monh-on-monh growh raes. The inspecion of he weighs shows ha, for insance, one monh of informaion already explains 66% of he quarerly growh rae of he indicaors. Hence, he low forecas errors and he similar performance of he various mehods should no come as a surprise. 5.2 GDP forecass under incomplee informaion: ou-of-sample resuls We now examine he performance of he various versions of equaion (1) under differen amouns of monhly informaion. For his purpose, we inser he forecass of q-o-q raes of monhly indicaors as obained in secion 5.1 ino various versions of he bridge equaions developed in secion 4. The resuls of his exercise are given in Table 5 for forecass of GDP growh in he curren and nex quarer. The main finding is ha he bridge equaions coninue o ouperform naïve and ARIMA forecass also when based on limied amouns of monhly informaion. For curren-quarer forecass his resul holds irrespecive of he mehod used for predicing missing monhly observaions. For nex-quarer forecass, however, we find a noiceable improvemen only if monhly indicaors are prediced from mulivariae models. The exrapolaion of monhly indicaors from univariae models, in urn, hardly improves upon a naive forecas for nex-quarer GDP. Among he mulivariae models, he BVAR performs slighly beer han he VAR, whereas he mulivariae STSM falls somewha shor of boh he VAR and he BVAR. We hus focus he discussion on GDP forecass based on VAR and BVAR models. For curren-quarer GDP forecass, he use of only one monh of wihin-quarer informaion (he 1 s curren-quarer forecas) provides already a considerably beer forecas for GDP han he naïve and ARIMA models. The RMSE from he quarerly ARIMA model amouns o 0.31 pp, compared wih values of around or even below 0.2 pp for he bridge equaions. For he 2 nd curren-quarer forecas, based on wo monhs of informaion, he RMSEs are hen generally very close o he final forecas. These findings are largely a direc consequence of he small curren-quarer forecas errors for monhly indicaors. I also worh menioning ha, alhough he relaive performance of he various bridge equaions, as discussed in secion 4, is largely mainained, ECN and OLI improve somewha in case of incomplee monhly informaion. ECN, in paricular, performs abou equally well compared o SW2. Turning o forecass for he nex quarer, he GDP forecass based on mulivariae monhly models sill improve considerably upon hose based on he univariae naïve and ARIMA models. For all models, he RMSE of he 1 s nex-quarer forecas, based on only one monh of wihin-quarer informaion (and wo monhs of daa for BCI and CR) remains below 0.3 pp, sill by some 25% lower compared o he naïve forecas. This forecas is carried ou around six monhs in advance of he official daa release. ECB Working Paper No 276 Sepember

21 Table 5 Ou-of-sample GDP projecion (Ou-of-sample RMSE from 1998 Q1 o 2001 Q4) Model for projecing monhly indicaors Univariae models Mulivariae models Naïve ARIMA STS MSTS VAR BVAR SW1 Nex quarer 1 s forecas nd forecas rd forecas Curren quarer 1 s forecas nd forecas rd forecas SW2 Nex quarer 1 s forecas nd forecas rd forecas Curren quarer 1 s forecas nd forecas rd forecas PCI1 Nex quarer 1 s forecas nd forecas rd forecas Curren quarer 1 s forecas nd forecas rd forecas ECN Nex quarer 1 s forecas nd forecas rd forecas Curren quarer 1 s forecas nd forecas rd forecas OLI Nex quarer 1 s forecas nd forecas rd forecas Curren quarer 1 s forecas nd forecas rd forecas Memorandum iems GDP growh sandard deviaion 0.37 GDP quarerly naïve forecas Nex quarer 0.37 Curren quarer 0.35 GDP quarerly ARIMA forecas Nex quarer 0.41 Curren quarer ECB Working Paper No 276 Sepember 2003

22 There arise some shifs in he relaive performance of he various equaions compared wih he resuls of Table 3. In general, he RSMEs from he paricular equaions end o be closer ogeher and he relaive performance of composie indicaors OLI and ECN improves. Furher, SW1 is slighly beer han SW2, conrary o wha is observed for curren-quarer forecass. Overall, ECN ends o perform bes. Alhough his resul should be viewed wih some cauion, given he relaively shor ou-of-sample forecasing period, i suggess ha he higher parsimony of equaions based on composie indicaors and he smooher evoluion of hose indicaors may improve he accuracy of nex-quarer GDP forecass. In paricular, he raher uninformaive forecass for CR and RS appear o hamper he performance of SW2. The OECD leading indicaor (OLI) falls somewha shor of oher indicaors, especially a shorer horizons. However, we had found in secion 5.1 ha he inclusion of OLI ino he VAR and BVAR improved he forecass for indusrial producion o a considerable exen. In fac, OLI has been developed as a leading indicaor for indusrial producion. The nex-quarer forecass based on univariae models, in urn, hardly improve upon he naïve forecas. The poenial gains from using monhly indicaors for nex-quarer forecass hus depend heavily on he predicabiliy of he indicaors. 6 CONCLUSIONS AND REMAINING ISSUES In his paper, we have examined he performance of bridge equaions o obain shor-erm forecass for euro area GDP growh from monhly indicaors. We find ha bridge equaions based on quaniaive aciviy indicaors (i.e. indusrial producion, reail sales and car regisraions) and, o a lesser exen, equaions based on composie indicaors resul in considerable improvemens in predicions for currenquarer GDP growh compared wih naïve or ARIMA projecions. The equaions provide informaive forecass also in case of incomplee monhly informaion. For insance, when based on only one monh of observaions, he roo mean squared error of he predicions amouns o abou 0.2 percenage poin, which compares o a value of 0.31 for he ARIMA forecas. The relaed monhly informaion becomes available during he las monh of he respecive quarer, some 2 ½ monhs in advance of he firs official release of GDP. Once unavailable monhly daa are forecas from mulivariae models, his improvemen also exends o predicions for nex-quarer GDP growh. In he laer case, EuroCOIN (Forni e al., 2001) and OLI indicaor (OECD, 2002) perform equally well as he equaions based on quaniaive indicaors. Somewha surprisingly, business survey daa however add no informaion o he above indicaors in forecasing GDP growh. Three imporan issues are lef for furher research. Firs, he coverage of he above quaniaive indicaors is largely limied o he indusrial and reail rade secors of he economy. The esimaes ECB Working Paper No 276 Sepember

23 presened in his paper could perhaps be significanly improved from he inclusion of monhly daa covering oher services secors as well. Second, we resriced he invesigaion o single bridge equaions. There migh ye be furher benefis in combining hese predicions wih projecions from quarerly simulaneous equaion models. Third, here arise a number of daa issues, relaed o he relaive performance of aggregae versus disaggregaed forecass and o daa revisions. Our sudy focused on aggregae euro area daa. The poenial benefis of a disaggregaed approach based on he aggregaion of individual counry forecass have no been assessed in his paper. The evidence for such benefis is quie mixed. Marcellino e al. (2003) repor ha forecass for key macroeconomic variables based on aggregae equaions are in general ouperformed by he aggregaion of individual counry forecass. In conras, Bodo e al. (2000) find ha an area-wide model for indusrial producion improves on he aggregaion of individual counry models. Clearly, as argued in Baffigi e al. (2002) and Hubrich (2003), while here migh be gains from he disaggregaed approach, such gains depend on he properies of he single counry specificaions and migh vary over he forecas horizon. The performance of he aggregae relaive o he disaggregaed approach also migh depend on he way he daa are consruced. Eurosa publishes seasonally and working-day adjused daa for GDP, which are aggregaed from already adjused counry daa. Raw daa are no available a he euro area level. In conras, for monhly indicaors, he adjusmen is direcly underaken a he aggregae level from raw counry daa. Maravall (1995) highlighs he possible disorive impacs of such differences in seasonal adjusmen procedures on he esimaed relaionships among series. Relaed o his, we have no invesigaed he issue of subsequen revisions o iniial daa releases and is poenial implicaions for real-ime forecasing performance eiher. The above forecasing exercises were carried ou wih daa series as currenly esimaed by saisical offices. In real ime, praciioners use daa, which would evenually be subsequenly revised. For aggregae euro area daa, due o a lack of backdaa on iniial daa releases, an assessmen on he role of daa revisions is pracically impossible. However, we are fully aware ha he resuls of his sudy may be alered wih he use of iniial daa releases. Indeed, for US daa, Croushore and Sark (2000) conclude ha findings on he relaive forecasing performance based on final daa releases do no necessarily carry over o real ime daa. Koenig, Dolmas and Piger (2001) go furher in his direcion and argue ha forecasing equaions should be raher esimaed from real-ime daa han from final daa releases. Taking hese caveas ino accoun, he above esimaes neverheless indicae ha early predicions of GDP based on an incomplee amoun of monhly informaion are a useful inpu ino real-ime conjuncural analysis. 22 ECB Working Paper No 276 Sepember 2003