International business cycle indicators, measurement and forecasting

Transcription

1 Research Deparmen Inernaional business cycle indicaors, measuremen and forecasing A.H.J. den Reijer Research Memorandum WO no 689 June 2002

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4 INTERNATIONAL BUSINESS CYCLE INDICATORS, MEASUREMENT AND FORECASTING A.H.J. den Reijer* * I would like o hank Peer Keus and Claudia Kerkhoff for saisical assisance. Moreover, I hank Bouke Buienkamp, Leo de Haan, Marga Peeers, Maaren van Rooij and Ad Sokman for useful commens and fruiful discussions. Research Memorandum WO no 689/02 June 2002 De Nederlandsche Bank NV Research Deparmen P.O. Box AB AMSTERDAM The Neherlands

5 Research Memorandum WO no 689/02 June 2002 De Nederlandsche Bank NV Research Deparmen P.O. Box AB AMSTERDAM The Neherlands

6 ABSTRACT Inernaional business cycle indicaors, measuremen and forecasing A.H.J. den Reijer In his paper he business cycles of nine OECD-counries are idenified by applying he Chrisiano- Fizgerald bandpass filer. Turning poins, recession and expansion phases and oher descripive saisics are derived from hese business cylce indicaors. Moreover, he inernaional linkage beween wo economies is invesigaed by measuring he degree of synchronism of he wo corresponding cyclical moions. In addiion o measuring he cyclical flucuaion, a composie leading indicaor is consruced which replicaes and predics he business cycle. This leading indicaor is a single index composed of economic, financial and expecaion variables possessing leading properies. The realime performance of he consruced business cycle indicaor for he Neherlands is compared o he performance of a similar indicaor based on he Hodrick-Presco filer mehodology. Key words: JEL codes: business cylces, urning poins, leading indicaors, bandpass filer, Forecasing C82, E32, E37 SAMENVATTING Inernaionale conjuncuurindicaoren, meing en voorspelling A.H.J. den Reijer In deze sudie worden de conjuncuurcycli voor negen OESO-landen geïdenificeerd door oepassing van he Chrisiano-Fizgerald bandpass filer. Van deze conjuncuurindicaoren worden omslagpunen, recessie- en expansieperioden en beschrijvende saisieken afgeleid. Bovendien word de inernaionale koppeling ussen wee economieën onderzoch door he bepalen van de mae van synchroniciei ussen de bijbehorende cyclische bewegingen. Aanvullend op he meen van de cyclische flucuaie word een samengeselde leidende indicaor geconsrueerd, die de conjuncuurcyclus repliceer en voorspel. Deze leidende indicaor is een enkelvoudige index en is opgebouwd ui economische, financiële en verwachingsvariabelen me leidende eigenschappen. De real-ime presaies van de geconsrueerde conjuncuurindicaor voor Nederland worden vergeleken me de presaies van een soorgelijk indicaor die is gebaseerd op de Hodrick-Presco filer mehodologie. Trefwoorden: business cylces, urning poins, leading indicaors, bandpass filer, Forecasing JEL codes: C82, E32, E37

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8 - - INTRODUCTION Under he second pillar of he ECB s moneary policy sraegy informaion on he cyclical posiion of he economy is an imporan elemen in he assessmen of he oulook for fuure price developmens. The cyclical insabiliy of aggregae economic behaviour will sooner or laer be refleced in similar paerns across various macroeconomic ime series. The cyclical moions of he variables are mosly simulaneous or in a rapid succession of one anoher. This phenomenon of leading and lagging cyclical behaviour over ime across macroeconomic variables can be exploied for he measuremen and forecasing of he conjuncural posiion of he economy. The economic sae of affairs is normally idenified as he cyclical sae of GDP. The sudy of business cycles, ha is of cyclical flucuaions in economic aciviy, goes back o he seminal conribuion of Burns and Michell (946), one of he earlies wriings on he business cycle. As a saring poin, i seems worhwhile o recall heir definiion: Business cycles are a ype of flucuaion found in he aggregae economic aciviy of naions ha organize heir work mainly in business enerprises: a cycle consiss of expansions occurring a abou he same ime in many economic aciviies, followed by similarly general recessions, conracions, and revivals which merge ino he expansion phase of he nex cycle; his sequence of changes is recurren bu no periodic; in duraion business cycles vary from more han one year o en or welve years; hey are no divisible ino shorer cycles of similar characer wih ampliudes approximaing heir own. This classical analysis describes movemens in acual economic ime series, in paricular he idenificaion of expansions and conracions in he absolue level of aggregae economic aciviy. Recen research in his spiri is performed by Harding & Pagan (2002b). In conras, mainsream modern lieraure invesigaes deviaion cycles, focussing on deviaions of economic aciviy from a long run rend. These are also called growh cycles in he lieraure, so ha growh expansions (growh conracions) are described when he growh rae is above (below) he long-erm rend rae of growh in aggregae economic aciviy, see for insance Canova (998) and Hodrick & Presco (980). As he business cycle is defined in erms of deviaions from rend, we will elaborae more on he naure and he properies of he filer used o esimae he long run rend. This research is originaed from he periodic revision of he currenly operaional business cycle indicaors a de Nederlandsche Bank. This sudy ulimaely aims firsly a idenifying growh cycles for 9 OECD-counries: he Neherlands, Belgium, Germany, France, Ialy, Spain, he Unied Kingdom, he Unied Saes and Japan. Secondly, we aim a forecasing hese business cycles by exploiing he early signals provided by leading indicaors. Afer measuring business cycles as deviaion cycles in GDP and indusrial producion, he cyclical movemen of a broad se of macroeconomic variables will be deermined. The resuling cyclical series are evaluaed on economic and saisical grounds and he accordingly seleced se of series forms he basis for he consrucion of a composie leading indicaor.

9 - 2 - The selecion crieria are amongs ohers a sufficien degree of similariy boh in erms of he moion of he business cycle and in erms of is urning poins and, secondly, leading properies wih respec o he business cycle. This composie leading indicaor provides herefore predicions of he business cycle. This procedure implies he invesigaion of many poenial ime series on leading properies. This research is no performed on a Euro area aggregae level for pracical reasons of daa collecion. The consrucion of such composie leading indicaors builds on he radiion of business cycle indicaor research a he Nederlandsche Bank, for insance Fase & Bikker (985), Bikker & De Haan (988), Berk & Bikker (995) and De Haan & Vijselaar (998). We will consruc indicaors along hese lines for nine OECD-counries wih special aenion o he Neherlands. Moreover, we will provide for each counry descripive saisics like he daing of business cycle urning poins, momen properies like he ampliude describing he severiy of he recessions and he srengh of he booms. These saisics are derived for each counry separaely. In addiion, he inernaional linkages of economic moions among counries can be measured by he fracion of ime wo economies are simulaneously in an economic upurn and/or a downurn. Finally, afer having measured he business cycle and consruced a leading indicaor for he Neherlands, he performance in real ime of his indicaor is invesigaed. For ha purpose we execue an ou-ofsample backes for boh he newly, in his sudy consruced, indicaor and he currenly operaional one as consruced by De Haan & Vijselaar (998).

10 - 3-2 MEASURING THE BUSINESS CYCLE The classical decomposiion of a ime series ino he componens rend, cyclical, season and erraic, is in fac deermined by he naure of he mehod of decomposiion used. The rend esimaion is no only specifying he long run moion of he ime series variable, bu implicily he remaining par of he series consising of he oher hree componens. There is a srand of lieraure dealing wih he quesion of how one should measure business cycles using differen rend esimaion echniques. For an overview of he comparaive properies of cyclical componens obained by using differen rend esimaors on a couple of common macroeconomic ime series, see for insance Canova (998). He concludes ha he exisence of a se of business cycle sylized facs ha is robus o varying rend esimaors is misleading, because differen conceps of a business cycle, and correspondingly differen rend esimaors, generae differen economic objecs which no necessarily have similar properies. However, alhough he second order properies, ha is he ampliude of he cycle, of he esimaed cyclical componens vary widely across derending procedures only minor differenial effecs emerge in higher momens. The concepual framework underlying business cycle analysis basically boils down o he quesion wheher an economic or a saisical based decomposiion should be used. The real business cycle lieraure is an example of he economics based decomposiion poin of view. Srucural ime series models are se up explicily in erms of componens ha have a direc inerpreaion, see Harvey & Jaeger (993). Consider for insance a srucural model where he unobserved permanen componen is a major cause of he business cycle. For example, a produciviy shock deermines boh long-run economic growh and he flucuaions around ha growh rend. So, removing his componen by filering ou a rend implies ha we are no longer examining business cycles, a leas according o he originally modeled business cycle concep. In fac, he rend-cycle dichoomy is only jusified if he facors deermining long-run growh and hose deermining cyclical flucuaions are largely disinc. However, here is no consensus on he precise sources of flucuaions. Even if ha would be he case, he quesions remain wha model appropriaely incorporaes hem and properly describes he propagaion mechanism urning hem ino acual business cycle paerns. The adherens of he saisical based decomposiion propose a so called measuremen wihou heory approach. The underlying concepual framework consiss of a se of saisical facs, such as he addiiviy propery ha a ime series is he sum of is consiuen componens and he condiion of orhogonaliy of hese For insance he componens rend, cyclical, seasonal and irregular. Consider he earlier menioned example of a produciviy shock, for insance he ICT-revoluion alledgedly shaping he new economy. Wheher his shock is a rend- or a cyclical one is an imporan quesion o be solved for a srucural model. Even if i is a rend shock, is he propagaion mechanism such ha he shock resuls in cyclical impulse responses? In he saisical approach he source and he propagaion of he shock are no an issue and he shock will only be a cyclical feaure o he exen ha he shock shows cyclical behaviour.

11 - 4 - componens o one anoher. So, he oal separaion of rend and cyclical behaviour in he observed ime series is saisically required. Pas research on he consrucion of De Nederlandsche Bank s business cycle indicaor belongs in his caegory by using a cenered moving average as rend esimaion mehod and laer on a Hodrick- Presco filer. This HP-filer has commonly been used in applied research, bu is since recenly suffering from severe criicism. For insance Cogley & Nason (995) criicise he HP-filer for inducing spurious cycles in filered ime series and argue ha he resuling sylized facs are herefore raher sylized arifacs. Moreover, he HP-filer has been criicized for resricing by consrucion he focus on paricular cycles wih an average duraion of 4 o 6 years, which is quie resricive compared o convenional definiions of business cycle periodiciies. The approach aken in his sudy elaboraes on his noion of defining business cycles as hose pars of a ime series consising of cycles wihin a paricular frequency band. The noion builds on he heory of specral ime series, which in he Specral Represenaion Theorem 2 saes ha any ime series wihin a broad class can be decomposed ino differen frequency componens. Moreover, he pars of a ime series belonging o disjunc frequency inervals are muually orhogonal. We can isolae he componen of a ime series associaed wih a frequency inerval by applying a linear ransformaion of he daa, which eliminaes all componens ouside his inerval. This procedure basically isolaes business cycle componens by applying weighed moving averages o macroeconomic daa. However, his moving average is of infinie order and an approximaion o his filer is necessary o be able o apply i on finie ime series. One such approximaion is given by Baxer & King (999) and consiss of an opimisaion under side consrains. The opimizaion consiss of minimising he squared difference of he exac and he approximae filer under he consrains, amongs ohers, ha firsly he applicaion of he filer resuls in a saionary ime series even when applied o rending daa. Secondly, he filer induces no phase shif which means ha i does no aler he iming relaionships beween series a any frequency by shifing he corresponding cycles forward or backward in ime. In he filer approximaion, here is a general rade-off involved: he ideal band-pass filer can be beer approximaed wih longer moving averages a he cos of dropping more observaions a he beginning and he end of he series, leaving fewer observaions for analysis. So, hirdly, he filer is required o be operaional in a pracical sense. An alernaive approximaion o he ideal band pass filer is derived by Chrisiano & Fizgerald (999). They perform he derivaion relaxing he consrains and using a differen weighing scheme 3 focussing on a pre-deermined frequency range. This resuls in a linear filer which uses all he daa 2 See Priesley (98) for a exbook on specral analysis and ime series. 3 A more deailed echnical descripion of boh he Baxer-King filer and he Chrisiano-Fizgerald filer can be found in he appendix.

12 - 5 - and which is more efficien in he sense ha i beer approaches he ideal band-pass filer. Moreover, hey demonsrae ha his efficiency gain comes a lile coss in erms of he filer rendering nonsaionary filered series and inducing phase shifs. For hese reasons in his sudy we will use he Chrisiano-Fizgerald band-pass filer o exrac business cycles from ime series. The Baxer-King band-pass filer (BKBP-filer) has been applied o business cycle research by, amongs ohers, Sock & Wason (2000) and Agresi & Mojon (200). As saed before he cyclical componen can be hough of as hose movemens in he series associaed wih periodiciies wihin a cerain range of business cycle duraions. A saring poin in defining his range of business cycle periodiciies is given in he inroducion s quoe saying beween one year and en or welve years. Sock & Wason and Baxer & King boh use he convenion of business cycles as variaions in GDP beween 6 and 32 quarers. This is based on he NBER business cycle reference daes whereby he shores cycle since 858 lased 6 quarers and he longes ones are mosly shorer han 8 years. Agresi & Mojon choose for he consrucion of an Euro Area business cycle a periodiciy band of.5 years and 0 years. They arrive a his higher upper bound by saing ha he euro area saw only hree recessions over he las hiry years. In addiion, he laes wo US-cycles lased more han eigh years. In his sudy we will adop he Agresi&Mojon convenion of business cycle frequencies. While GDP ges mos aenion from forecasers and provides a broader coverage of he economy we will use, like in Berk & Bikker (995) he manufacuring oupu volume as he reference series from which he business cycle indicaor is filered. The producion of manufacuring indusry represens roughly only a quarer of GDP. However, some expendiure componens of GDP are ypically noncyclical or even couner-cyclical possibly wih differen leads and lags. Governmen expendiure, for example, does no follow he general economic cycle. The social securiy sysem acs as an auomaic sabilizer and ends o be couner-cyclical and lagging he cycle. From a pracical poin of view, GDP is only available on a quarerly basis, he publicaion lag is considerably longer han for manufacuring oupu daa and he revision of GDP numbers afer he firs publicaion is considerably larger. As predicing he business cycle is one of he main purposes, an up o dae business cycle figure is deemed essenial. The consrucion of he business cycle indicaor consiss of applying he Chrisiano-Fizgerald filer o he manufacuring oupu series and sandardising he resuling cyclical paern. The resuling business cycle indicaor for he Neherlands is graphed in figure. The firs figure shows he seasonally adjused GDP-ime series, he Chrisiano-Fizgerald rend and he resuling cyclical paern. The second picure shows he sandardised cyclical paern which is called he business cycle indicaor. The urning poins are derived from his indicaor according o a procedure oulined below. The periods beween a peak and a rough are he recession periods and are indicaed in all hree graphs by he shaded area. The hird graph shows he resemblance of recession periods defined by our mehods

13 - 6 - and he more commonly used year-on-year GDP-growh numbers. Recession periods correspond o declining growh raes and vice versa. The beginning and one period afer he ending of he recession

14 - 7 - period are he business cycle urning poins. A he hear of daing cyclical urning poins is he sandard calculus rule for finding exreme values, i.e. seing he firs derivaive of he ime series variable y wih respec o ime equal o zero: dy/d=0. A modified rule is needed in a discree seing ha is ypical for macroeconomic ime series. A local peak in indusrial producion, y, occurs a ime if y exceeds values y s for -k<s< and +k>s>, where k delineaes some symmeric window in ime around. This simple idea is he basis of he NBER procedures summarized in he Bry & Boschan (97) daing algorihm. In pracice, he Bry-Boschan algorihm wih k=5 for monhly daa also applies some censoring rules ensuring a minimum cycle duraion of 5 monhs and alernaion of peaks and roughs. This algorihm has been applied on ime series daa in levels and so produces he daing of classical business cycles. Now consider he growh cycle ime series variable BCI =y -g. The variable BCI is now he deviaion of indusrial producion, y, form is long run Chrisiano-Fizgeraldrend, g, and a similar urning poin algorihm can be applied on his deviaion series. The Bry- Boschan algorihm has been adaped by Dungey & Pagan (2000) o dae growh cycles. We perform our daing in his spiri and apply an algorihm ha follows he following rules: -peaks and roughs mus alernae, -a peak (rough) mus represen above (below) rend growh and so he corresponding z >(<)0, -he urning poin mus be a local opimum a peak a if (BCI -p,,bci - <BCI >BCI +,,BCI +q ), BCI >0 for [-p,,q], () a rough a if (BCI -p,,bci - >BCI <BCI +,,BCI +q ), BCI <0. for [-p,,q]. The business cycle indicaors of he nine counries are calculaed by applying he Chrisiano- Fizgerald filer and sandardising he resuling cyclical series. Subsequenly, he business cycle daing is performed by applying he abovemenioned daing rules o he business cycle indicaors. The daing procedure provides he collecion of daes a which he business cycle indicaor reaches a peak or a rough. A conracion (expansion) period is sraighforwardly defined as he period beween a peak (rough) and a rough (peak) indicaing declining (increasing) growh raes. The business cycle indicaors ogeher wih he conracion periods for he nine counries are shown over a subperiod in he graphs of appendix B. The business cycles are represened by he hick lines and he conracion periods by he shaded areas. The resuling wo lines will be explained in he nex secion. In order o derive descripive saisics for he business cycle indicaors we consruc a sae variable S, which equals one in conracion periods, he period from one monh afer he peak dae o he dae of he rough, and zero oherwise. The informaion {BCI,S } provides a picure of he characerisics of he cyclical moion and can be used o produce descripive saisical measures like duraion, ampliude, seepness and sharpness of expansion and conracion phases. We will use he descripive saisics for he business cycle indicaors of Harding & Pagan (2002b). We need o keep in mind ha he saisics describe wha he indicaors measure. By consrucion, he business cycle indicaors are he deviaion of he log of indusrial producion series from is long run Chrisiano-Fizgerald rend.

15 - 8 - Because he daa is used in logs he indicaor represens percenage deviaions from rend. So, he saisics describe he cyclical behaviour of indusrial producion and only serve as an approximaion o cyclical behaviour of GDP (-growh) o he exen ha he cycles in indusrial producion correspond o cycles in GDP. The mos commonly used descripive saisics are he sandard deviaion, skewness and kurosis. The sandard deviaion measures he variabiliy of he indicaor. Skewness measures he one-sided faailedness of he probabiliy disribuion of he indicaor. So, i measures wheher expansions are relaively more exuberan han ha conracions are severe. Kurosis measures he wo-sided faailedness and indicaes wheher large cyclical movemens are relaively more common. The sae variable S separaes expansion and conracion phases. A peak occurs a ime when S = and S + =0. An expansion (conracion) phase consiss of he periods beginning wih he monh afer he dae of a rough (peak) and ending a he dae of a peak (rough). Expansions and TP (rough-opeak) and conracions and PT (peak-o-rough) will be used inerchangeably. The average duraion 4 of expansions and conracions are: = DUR PT = T, (2) ( S+ ) = T S S ( S ) ( S ) = T = DUR TP = T. (3) S + The numeraor in (2) measures he oal ime spen in conracions and he denominaor couns he number of peaks. The average ampliude sraighforwardly equals: T S BCI = AMP PT = T, (4) S ( S+ ) = 4 In calculaing average of expansion and conracion phases one has o deal wih uncompleed phases a boh end of he sample. In his sudy we base he saisics on compleed phases and hen he summaion runs from he beginning of he firs compleed phase unil he end of he las one raher han over,,t.

16 - 9 - T ( S ) BCI = AMP TP =. (5) T S ( S ) = + Thinking of a phase as a riangle wih as base is duraion and as heigh is ampliude, hen he seepness of a phase is naurally measured by he slope of he riangle: STEEP = AMP. (6) DUR In addiion o looking a he seepness over he phases one migh wan o compare he shape of he cycle in he early par of he cycle wih ha in he laer par. A simple way of capuring his shape is o divide a phase ino wo pars and o compare he average growh raes in he firs par o ha in he second par. This saisic is called sharpness and essenially measures a degree of convexiy of he indicaor, ha is he relaive seepness of he early sage in he business cycle. Le i be he i h phase and d i be he duraion of his phase, saring in ime i. The measure of he shape of a single phase can hen be defined as: v i d i 2 di = ( BCIk+ BCI + ) i k i d i 2 k= k= di ( BCI BCI ) 2 + k+ i k+ i. (7) Thus, if in an expansion phase, growh is faser in he firs half of he phases duraion han in he second half, hen his measure will be posiive. If in a conracion phase he decline is slower in he firs half of he phases duraion han in he second half, hen his measure will be posiive. If a cyclical indicaor shows hese wo posiive measuremens i implies ha he peaks are relaively long lasing and rounded and he roughs are relaively shor lasing and poined. Averaging (7) over all similar phases can be defined as: SHARP SHARP PT TP d v i = i i S j j i ( S j ), (8) d v. (9) j = i i Equaions (8) and (9) are in effec weighed moving averages of he appropriae form of (7). The weigh for a paricular expansion is he duraion of ha expansion divided by he oal sum of he

17 - 0 - indicaor being in an expansion phase. So, his weighing scheme gives more weigh o longer phases and he sum of he weighs equals one. The descripive saisics for he nine business cycle indicaors are presened in Table. Almos all counries display kurosis indicaing ha large cyclical movemens are relaively common. The Neherlands and o a lesser exen Belgium sand ou on sabiliy, bu no on moderaeness. Sabiliy is revealed by he volailiy of he cyclical behaviour around he rend and by he ampliude. This is he absolue deepness of a cycle decomposed in conracion and expansion phases. Boh he Neherlands and Belgium show he lowes numbers for all nine counries on he sandard deviaion and he ampliude. Moderaeness is revealed by he seepness saisic. Seepness can be inerpreed as he moion deepness of a conracion or expansion phase like ampliude can be seen as he absolue deepness of a conracion or expansion phase. For boh phase ypes, he Neherlands and o a lesser exen Belgium show among he highes numbers for he seepness saisic indicaing ha boh economies move quickly from one urning poin o anoher. Japan acs as he mirror image of hese wo counries by showing he highes cyclical volailiy and he highes cyclical severiy boh in erms of ampliude and seepness for boh conracion and o a lesser exen expansion periods. The Unied Saes also display high cyclical volailiy and severiy. The negaive skewness indicaes conracion phase ouliers indicaing a relaively severe recessions. The large conracion sharpness and he large expansion sharpness for he U.S. reveals a paern of smooh rounded peaks and poined deep roughs. Ialy demonsraes he larges posiive skewness and among he highes peaks, ha is he average ampliude of he expansion phase. Boh saisics indicae large upward cyclical ouliers. The quie moderae sharpness saisic reveals ha he Ialian cyclical paern surrounding urning poins is paricularly smooh. Germany shows a relaively long expansion phase compared o he conracion phase. On he oher hand he conracion phases moion is relaively fas according o he seepness saisic and relaively deep according o he negaive skewness. The sharpness saisic reveals ha he German urning poins are he mos sharply poined ones of he nine counries. Therefore, he German indicaor looks somewha like a saw ooh.

18 Table Summary saisics for he business cycle indicaors, 965:-200:9 Sandard Skewness Kurosis Duraion Ampliude Seepness Sharpness deviaion PT TP PT ) TP PT ) TP PT TP Neherlands Belgium France ) ) Germany Ialy ) ) Spain Japan ) ) Unied Kingdom ) 0.0 2) Unied Saes Noes: he saisics represen he deviaions from rend series which are no sandardised. The mean of he deviaion cycle is by consrucion approximaely zero. So, sandardising comes down o dividing he deviaion ime series by is sandard deviaion. PT means he phase Peak-o-Trough and is herefore synonym o conracion phase. Even so is TP synonym o expansion phase. The skewness measure is µ 3 /(µ 2 ).5 and he kurosis measure is µ 4 /(µ 2 ) 2, where µ r is he r h cenral momen. The skewness of a symmerical disribuion, such as he normal, is zero. Similarly, he kurosis of he normal disribuion is 3. ) he numbers are presened wih opposie signs for he sake of comparison wih expansion periods. 2) hese numbers are muliplied by 00.

19 - 2 - Now ha he Euro area is composed of a number of counries for which individual counry cycles are available i is ineresing o go beyond examining individual cycle characerisics and analyse he relaionships beween hese business cycles. More precisely, we wan o examine how closely he cycles of individual counries are synchronized o one anoher. A popular index ha has been proposed for his ask, Harding & Pagan (200a), is he index of concordance, which measures he fracion of ime ha wo business cycles spend in he same phase. Le S i and S j denoe he sae variables of he business cycles of counry i and j. The index of concordance is defined as: IC ij = T T i j i j { S S + ( S )( S )} =. (0) For all nine counries he resuls for he index of concordance are presened in he upper riangle of Table 2. The ialic numbers in he lower riangle are he cross correlaion coefficiens of he wo concerning business cycles. Six of he nine counries examined in his sudy are par of he Euro area. These six counries can form 5 unique couples 5 which provides 5 indices of concordance (ICs) measuring Euro area business cycle synchronisaion. The average of hese 5 indices is 0.74 and he average correlaion is As can be calculaed from able 2, wo Euro area counries are on average roughly hree quarers of he ime in he same conjuncural sae. Boh he correlaion and he IC of he big Euro area counries Germany and France are jus 0.68 and hose beween Germany and Ialy only 0.32 respecively The average IC and correlaion of he poenial Euro area member he Unied Kingdom and he five Euro area counries equal 0.64 respecively 0.56, which is even worse han he average IC of 0.67 beween he Unied Saes and he Euro area counries and slighly beer han he average correlaion of 0.54 beween hese wo economic blocks. Moreover, he IC and he correlaion beween he Unied Kingdom and he Unied Saes equal 0.75 and 0.7 respecively. This indicaes ha he Unied Kingdom s business cycle is more synchronised wih he Unied Saes one han wih he cycle of he Euro area. 5 Of course, one can consruc an index of concordance which only measures he simulaneiy of more han wo counries ogeher. I hen measures he fracion of ime ha all counries are in he same sae. For example, he concordance of Germany, France and Ialy ogeher is 0.57

20 - 3 - Table 2 Business cycle indicaors correlaion and index of concordance NL BE FR GE IT SP JP UK US NL BE FR GE IT SP JP UK US Noe: The sample period is 965:-200:9. The indices of concordance are represened in he upper riangle of he able. The correlaion coefficiens are represened in ialic in he lower riangle of he able. The counry abbreviaions are as follows: Neherlands (NL), Belgium (BE), France (FR), Germany (GE), Ialy (IT), Spain (SP), Japan (JP), Unied Kingdom (UK) and Unied Saes (US).

21 - 4-3 HOW TO REPLICATE AND PREDICT THE BUSINESS CYCLE Cyclical moion in he economy is refleced in varying macroeconomic ime series. In he previous secion he business cycle is idenified as he cyclicaliy of indusrial producion. This provides a signal for he curren sae of he economy. By naure of he macroeconomic sysem, variables can be classified as leading, coinciden or lagging dependen on he iming behaviour of heir cyclicaliy visà-vis he business cycle indicaor. Leading variables give by naure an early signal on he conjuncural posiion of he economy. We will exploi his feaure by selecing a se of leading variables and ransforming hem ino a single composie leading indicaor, which replicaes and predics he business cycle indicaor. Poenial leading variables which, from an economic poin of view, can be expeced o lead and predic he general business climae are gahered and will be called basic indicaors. Moreover, candidae variables mus fulfill pracical crieria like availabiliy of long ime series wih as few inerrupions and definiion aleraions as possible and availabiliy of daa wih minimum delay. The cyclical pars of all basic indicaors are compared o he business cycle indicaor in order o deermine he numbers of monhs by which he basic indicaors lead he business cycle, i.e. he iming. The firs measure of his iming is he lead (-l) in number of monhs corresponding o he maximum cross correlaion coefficien beween he business cycle indicaor (BCI) and he lagged basic indicaor (BI): 2 ( ) ( l) = ( BCI BCI )( BI l BI l ) ( BCI BCI ) ( BI + l BCI l ) ρ () l = arg max ρ l ( l) + (2) In formula () BCI and BI l are he averages of BCI and BI +l respecively, over. The magniude of he correlaion coefficien () measures he degree of cyclical similariy of he business cycle indicaor and he basic indicaor. Moreover, he corresponding lead of l is measured in (2) and represens he opimal lead of he basic indicaor. The wo indicaors resemble he mos similar moion a his lead because of he maximisaion procedure and he definiion of he correlaion coefficien. A second resricion concerning he lead is he maching of urning poins of he wo series. The ulimae composie leading indicaor is no only supposed o reflec he moion of he business cycle indicaor, bu also o provide an early signal of upcoming urning poins. The opimal lead obained from (2) will herefore be fine-uned by maching peaks and roughs of boh series more closely. The algorihm execuing his ask consiss of idenifying urning poins as saed in (), maching he peaks and roughs of he business cycle indicaor o neares ones of he basic indicaor, which is shifed by he lead l, and finally fine-uning his lead by adjusing i in order o minimize a disance meric. This

22 - 5 - meric is sraighforwardly he sum of he disances measured in monhs beween all peaks and roughs of he business cycle indicaor and he corresponding peaks and roughs of he basic indicaor. Boh he cross correlaion () and he fine-uned version of (2) ac as saisical crieria for he selecion of he leading indicaors ha ogeher consiue he basis of he composie leading indicaor. Analogous o Bikker & Berk (995), a poenial leading indicaor should show a cross correlaion () of a leas 0.5 and a minimum fine-uned lead (2) of 6 monhs in order o be seleced. These boundaries are chosen as high as possible under he resricion ha a sufficien number of leading indicaors be seleced. The aim is o ransform he seleced basic leading indicaors ino a single composie index which replicaes and predics he business cycle indicaor. The replicaion propery is ensured by () and he procedure of maching urning poins. The predicion propery is ensured by he crierion of minimum lead. A single composie index possessing boh properies is hen consruced as an opimal linear combinaion of normalised and synchronised seleced basic leading indicaors. Normalisaion means ransforming he basic indicaor such ha an indicaor showing zero mean and uni sandard deviaion resuls. This normalisaion procedure makes indicaors exhibiing weak cyclical variaion, for insance wages, comparable o indicaors exhibiing srong cyclical variaion, for insance confidence indicaors and prevens he laer ones from dominaing he former ones in a single composie index. The seleced leading indicaors are synchronised wih he business cycle indicaor by shifing hem forward by heir respecive leads. This synchronisaion procedure aligns he leading indicaors cyclical phases wih he business cycle indicaor s one and causes heir urning poins o coincide on average. Shifing a leading indicaor variable forward by a number of monhs equal o is lead means ha he shifed leading indicaor variable no longer leads, bu insead coincides wih he cyclical phase of he oal economy. Because of he shifing however, he series exends beyond he observaion period and provides a predicive signal for he near fuure cyclical developmen. Afer applying normalisaion and synchronisaion each seleced leading indicaor provides is own early signal. A one-dimensional single signal is obained by consrucing an opimal linear combinaion of he individual normalised and synchronised leading indicaors by means of principal componen analysis. The firs principal componen is he common elemen in he se of seleced leading indicaors and is supposed o be a reflecion of he business cycle indicaor. Principal componen analysis ensures ha here is no oher linear combinaion of he leading indicaors which will accoun for more of he inrinsic oal variance of he se of leading indicaors han he firs principal componen. So his componen represens he mos common moion across he se of leading indicaors.

23 - 6-4 EMPIRICAL RESULTS ON THE LEADING INDICATORS To perform he procedures of he previous secion a collecion of poenial leading variables is compiled consising of abou 40 monhly ime series for each counry. These variables are esed by calculaing he opimal values for () and (2). The resuls are presened in Table 3. The firs number in each cell is he opimal lead and he second number is he maximum cross correlaion for he concerning leading indicaor and counry. The seleced leading indicaors are of an economic, financial and moneary naure and confidence and expecaions surveys. Of he economic flow variables consumpion, invesmen, expors and impors only in Japan consumpion shows a leading cyclical paern. Consumpion can sraighforwardly be seen as a demand-pull rigger for economic aciviy 6. Ani-cyclical governmen consumpion and influencing privae consumer behaviour by ax inducemens are par of he Keynesian recipe. Invenories are a resul of non-maching economic flows and for mos counries he sorage of final producs provides an early signal for producion aciviy. According o De Haan & Vijselaar (995) here exiss a oneway Granger-causaliy from he sorage of final producs owards indusrial producion for he Neherlands. A second ype of invenories are hose a he sar of he producion process, like he level order posiions and issued building permis. Boh variables procyclically lead he business cycle. Prices and wages are a fundamenal par in every economic model describing cyclical flucuaion. Following Sock&Wason(2000), a general paern emerges of leading, counercyclical price levels and lagging, procyclical raes of inflaion. The nominal wage index exhibis a paern quie similar o consumer prices, probably due o he conracual indexing of wages. Consumer prices, sales prices, oal wages and hourly wages emerge in his sudy as business cycle leaders. Moreover, labour coss per uni produc is a combinaion of wages and produciviy and on average leads he cycle counercyclically. The same paern shows up for he world marke prices of commodiies, which basically is a cos variable for producion. A dominan class of leading variables concerning business cycles are hose specifically relaed o he fuure. These variables are he resul of surveys and he following are idenified o procyclically lead he general cycle: consumer and producer confidence, expeced fuure indusrial producion, prospecs oal economy, judgemen of order arrivals and he IFO-indicaor 7 for Germany. Financial variables deal wih he purchasing and invesmen possibiliies and herefore also wih he choices made by privae and public agens. As he sum of discouned expeced fuure cash flows share prices are, like surveys, fuure linked variables. They parly deermine he budge consrain and can 6 Think of he appeal of he Bush adminisraion o he American people following he Sepember -aacks o consume he U.S. ou of a recession. 7 We choose a subindex of he IFO-indicaor which refers o fuure developmens.

24 - 7 - herefore ac, unlike surveys, as a caalys for a mechanism of self-fulfilling prophecy. Financial markes expecing an upurn creae he possibiliies for an upurn. Ineres raes are a cos of capial and herefore also parly deermine he budge consrain. Boh shor erm and long erm ineres raes lead he business cycle wih posiive values of ineres raes associaed wih cyclical declines in oupu. The lead of he shor erm ineres rae is approximaely.5 years for mos counries o over wo years for Japan, see able 3. The connecion beween shor erm ineres rae movemens and he oupu gap is esablished in he Taylor rule. The spread beween he shor and long erm ineres raes has long been recognised as a leading indicaor. An invered yield curve, ha is shor raes exceeding long raes, anicipaes subsanial declines in economic aciviy. However, given i s widely acknowledged predicive poenial we prohobi aking his variable ino he model ogeher wih boh he shor and he long erm ineres raes. Moneary aggregaes play an imporan role in he deerminaion of price levels and can resul in movemens of real quaniies because of nominal fricions in he economy. Following he ime inconsisency lieraure, in he shor run a moneary expansion creaes a boos in employmen and oupu and in he long run only causes a rise in he price level. We basically consider hree moneary aggregaes, namely if available M, M2 and M3 and boh es hem in nominal and real erms and in levels and growh raes. We however find only for Spain a moneary aggregae funcioning as a leading indicaor. Sock & Wason (998) noe ha he conamporaneous cross correlaion beween he cyclical componens of nominal M2 and oupu has drasically declined since he early eighies for he Unied Saes. The seleced basic leading indicaors are composed ino one single composie leading indicaor by means of principal componen analysis as oulined in he previous secion. In figure A in he appendix he business cycle indicaor ogeher wih he composie leading indicaor are graphed for each counry. By selecion he basic leading variables are by selecion leading he business cycle by a leas 5 monhs and he composie leading indicaor is herefore by consrucion also leading he business cycle wih 5 monhs. The correlaion coefficien beween he business cycle indicaor and he composie leading indicaor are displayed for each counry in he las row of Table 3. In figure A2 in he appendix he seleced basic variables used o consruc he composie leading indicaor are graphed for he Neherlands. In each single graph he raw imes series and he rend are ploed ogeher wih he resuling sandardised cyclical par.

25 - 8 - Table 3 Resuls of selecion leading indicaors Neherlands Belgium France Germany Ialy Spain Japan Unied Kingdom Consumer confidence Consumer price index* World marke 8 5 prices commodiies* M* Equiy price Shor erm ineres 9 rae* 0.5 Long erm ineres 8 rae* 0.53 IFO Expeced business 6 aciviy 0.84 Expeced fuure indusrial producion Sorage final producs* Prospecs oal 0 economy Judgemen of order arrivals Level order posiion Hourly wage indusry* Domesic sales prices* Producer confidence Consumpion Toal wages* Labour coss per uni produc* Unied Saes Correlaion Coefficien beween business cycle and leading indicaor Noe: The firs number in each cell is he opimal fine-uned lead (2) and he second number is he maximum correlaion () of he corresponding variable. The variables marked wih a * counercyclically lead he business cycle insead of procyclically. The saisics presened in his able are, excep for he Neherlands, based on he cyclical moions of he variables filered wih a lowerbound of 36 insead of 8 monhs and an upper bound of 20 monhs. All counries possess a minimum lead of 6 monhs, excep for he Neherlands, France and Germany. These hree counries possess a lead of 5 monhs. De correlaion coefficien beween he business cycle and he leading indicaor should be read wih cauion, because he leading indicaors are also consruced on he basis of urning poin congruency.

26 - 9-5 COMPARING BUSINESS CYCLE INDICATORS FOR THE NETHERLANDS In his sudy we have oulined a mehodology and consruced accordingly business cycle indicaors and composie leading indicaors for nine counries. In his secion we will provide a comparison beween he consruced indicaor for he Neherlands and he indicaor as consruced by De Haan & Vijselaar (998). We will refer o his indicaor as Hodrick-Presco, because his filer mehodology was used for rend esimaion. Addiional o a differen mehodology, he Hodrick-Presco leading indicaor is parly based on differen basic leading indicaors. I is based on he real moneary aggregae M and he yield curve, which are boh no used by he newly consruced indicaor. The IFO-indicaor for Germany, expeced business aciviy and he shor-erm ineres rae are basic leading indicaors used by boh he newly consruced and he Hodrick-Presco indicaors. The wo business cycle indicaors and he wo leading indicaors are graphed in figure 2.

27 Boh mehodologies rack a quie similar picure of he pas conjuncural posiion of he Duch economy. Alhough eiher indicaor produces broadly an equal cyclical shape, deail differences remain. Table 4 provides he daing according o () of he business cycle urning poins for boh mehodologies. The bigges urning poin dae difference beween boh indicaors is 3 monhs, namely beween he rough daing of Ocober 984 and November 985 for Hodrick-Presco and Chrisiano-Fizgerald respecively. Table 4 Turning poin daing for he Neherlands Hodrick-Presco Chrisiano-Fizgerald July 967 June 967 Augus 970 December 969 May 972 January 972 March 974 March 974 June 975 July 975 Ocober 976 Augus 976 January 978 July 977 Ocober 979 November 979 April 983 December 982 November 985 Ocober 984 December 987 November 987 April 990 Augus 990 July 993 July 993 June 995 February 995 Augus 996 January 997 February 998 January 998 November 998 February 999 July 2000 Ocober 2000

28 - 2 - The measuremen accuracy of he cyclical moion mainly depends on he filer used for he rend componen. The difference beween he rend esimaions of he newly consruced indicaor based on he Chrisiano-Fizgerald bandpass filer and he exising indicaor based on he Hodrick-Presco filer is graphed in figure 3. This figure plos a monhly ime series of he year-on-year growh raes of boh rend mehodologies. I follows ha rend growh is abou 5% in he sixies and 2.5% o 3% in he lae sevenies, eighies and nineies. Moreover, i clearly shows ha he Hodrick-Presco filer akes up much less of he cyclical moion han he Chrisiano-Fizgerald one. In erms of bandpass filering, applying he Hodrick-Presco filer resuls in a cyclical componen incorporaing cycles lasing longer han 0 years. All filers face he end poin problem. This means ha hey canno provide accurae esimaes of he real-ime rend and he real-ime cyclical posiion unless daa is available for he enire curren cycle. A real-ime esimae is an esimae on he dae for which he laes observaion is available. An imporan feaure from a forecasing perspecive is he behaviour of he indicaor in real-ime. More specifically, wha is he difference beween he indicaor a ime given daa unil ime, BCI and he indicaor a ime given daa unil ime T (T>), BCI T. This difference is called he revision error and is purely caused by he ineviable end poin problem of he filer mehodology. The mean absolue revision error is defined by: MARE n = T 60 ( ) T 20 n BCI BCI (3) = 6 n + n T In (3) he firs and las 60 observaions of he sample are disregarded in order o avoid a bias. The underlying assumpion is ha he cyclical moion has reached is definie, never changing shape afer having addiional daa available for a half cycle, ha is 5 years. The validiy of his assumpion sems from Table 5, where mean absolue revision errors are displayed for differen values of n. This parameer represens he number of addiional available daa a ime for he calculaion of he business cycle a ha ime. The able clearly shows he expeced decline of he revision error as more daa becomes available for he Chrisiano-Fizgerald filer. The Hodrick-Presco mehodology shows a deerioraion afer a few addiional daa and subsequenly a much more definie cyclical shape. The iniial deerioraion is probably due o he eliminaion procedure of he seasonal componen. The more definie cyclical shape is shown by he lesser MARE when more han a year of exra daa is available. This phenomenon can be explained by he lesser cyclicaliy of he Hodrick-Presco filer due o he iniial parameer seing as shown in figure 3. Incorporaing cyclical flucuaions of duraion of more han 0 years in he rend esimaion causes much more volailiy of his rend and herefore for he resuling cyclical moion when more and more daa becomes available.

29 A second feaure of he end poin problem is he urning poin dae insabiliy. This refers o he change in he daing of a urning poin when more and more daa becomes available. The iniial dae of a urning poin is he firs idenified dae corresponding o a specific urning poin. The iniial daing urns ou o be robus is a urning poin is defined by () wih p=q=3. Only if urning poins are relaively rounded, like he one in 990, he urning poin dae is quie flucuaing unil he exac one is esablished. Moreover, i holds for boh algorihms ha false signals are absen if one disregards he subcycle of 982. Table 5 Revision errors for he indicaors of he Neherlands MARE 0 MARE MARE 3 MARE 6 MARE 2 MARE 36 MARE 60 BCI HP BCI CF Noe: MARE n is defined in (3). BCI HP is he business cycle indicaor for he Neherlands based on he Hodrick-Presco mehodology. BCI CF is he business cycle indicaor for he Neherlands based on he Chrisiano-Fizgerald mehodology. This laer mehodology is slighly modified by aking moving averages up o 60 periods. More precisely, for i= 60 he indicaor BCI -i is he average of BCI -i -i+j for j=,,i. This is done o average ou seasonal and end poin effecs.

30 CONCLUSION In his sudy we idenified business cycles in deviaions from rend for nine OECD-counries. We used a bandpass filer o esimae he rend and he cyclical componen of a ime series. The moion of a ime series wihin an a priori specified frequency inerval can be isolaed by applying a bandpass filer. Each bandpass filer requires an opimisaion for dealing wih finie ime series. The Chrisiano- Fizgerald bandpass filer uses all available daa o calculae he filer weighs and herefore provides a more efficien esimae han he well-known Baxer-King bandpass filer. We adop he convenion ha a business cycle consiss of all cycles wih duraion longer han 8 monhs and shorer han 0 years. The business cycle indicaor is consruced applying he filer on he producion of manufacuring indusry series. Business cycle urning poins and recession and expansion periods are derived from he indicaor. Moreover, a range of summary saisics is provided describing feaures like ampliude, seepness and duraion of he cycle for each counry. The Neherlands and o a lesser exen Belgium sand ou compared o he nine counries on sabiliy by showing a relaively modes cyclical spread around he rend. Their cyclical moions are however he leas moderae so ha boh economies move quickly from conracion o expansion phases and vice versa. Japan acs as he mirror image by showing he larges cyclical swings. The U.S. reveals a paern of smooh rounded peaks and poined deep roughs. The inernaional linkage beween economies is explored by calculaing he fracion of ime he wo economies are eiher boh in he expansion phase or boh in he conracion phase. This saisic shows ha he Unied Kingdom is more synchronised wih he Unied Saes han wih he Euro area. The average synchronisaion beween he Unied Kingdom and he Euro area counries is lower han he average synchronisaion of he Euro area counries wih one anoher. In addiion o measuring cycles we consruced a single composie leading indicaor, which replicaes and predics he business cycle. The leading indicaor is based on economic, financial and survey variables possessing leading properies. These variables are seleced from a se of 40 candidae variables for each counry. The variables ha have been seleced for five or more counries are he shor erm and long erm ineres raes, he sorage of final producs, he hourly wages, he domesic sales prices, he IFO-indicaor for Germany and he consumpion price index. The business cycle indicaor for he Neherlands shows a similar picure of he pas conjuncural posiions as he curren operaional indicaor a De Nederlandsche Bank. This indicaor is based on he Hodrick-Presco filer mehodology. I possesses a rend which capures less cyclical variaion han he Chrisiano-Fizgerald rend wih a lower bound of 0 years. The performance in real-ime of boh