A New Indicator Based on Neftçi s Approach for Predicting Turning Points of the Euro-Zone Growth Cycle*

Transcription

1 Viereljahrshefe zur Wirschafsforschung 7. Jahrgang, Hef 3/2 S A ew Indicaor Based on efçi s Approach for Predicing Turning Poins of he Euro-Zone Growh Cycle* By Jacques Anas and Muriel guiffo-boyom** Summary "[...] in many siuaions a decision does no have o be made immediaely, bu can be delayed unil addiional informaion has been acquired. Sequenial analysis seems paricularly applicable o he problem of predicing urning poins in he business cycle" (Palash and Radeci, 985). Elaboraing on his idea, we propose a new approach o predic cyclical urning poins in he Euro-zone using he efçi s approach. The oupu is a probabiliy index for a forhcoming economic urning poin.. Inroducion If here is a large lieraure on he analysis of economic flucuaions, here has been a renewed ineres in cycle analysis and indicaors in he pas years due o he emergence and developmen of new innovaive non-linear mehods. However, he idenificaion of economic flucuaions in real ime and he predicion of economic urning poins raise various specific issues and may herefore involve differen approaches. In shor, he bes model o explain he business cycle may no be he bes model o predic. In a Bayesian framewor a priori informaion may be used o improve he performance of predicive indicaors. This paper presens a new approach o deec and predic urning poins. Is validiy is evaluaed hrough an expos performance assessmen. The efçi (982) sequenial probabilisic formula is applied o deec urning poins in ime series. In his paper we shall focus on a Euro-zone indicaor. Wih he Economic and Moneary Union (EMU), European counries are facing a common moneary policy carried ou by he European Cenral Ban (ECB) despie he heerogeneiy of heir economic performances. The objecive of he ECB is o mainain he Euro-zone inflaion under a fixed arge of 2%. The economic heerogeneiy is visible firs a he level of real economic aciviy if we loo a differen saisics lie GDP per capia, growh or poenial growh. More recenly, we have winessed a divergence in he inflaion paerns. Asymmeric inflaion raes beween EMU counries are a sympom of European srucural dispariies (mare good or labor rigidiies, sensibiliy o exernal inflaion) and cyclical differences. Since he ECB has a unique inflaion arge for he Eurozone, i appears useful o build a leading indicaor of Eurozone cyclical urning poins, which should be helpful for any cyclical diagnosis of he Zone. In our sudy, we chose o focus on he six major counries (Belgium, France, Germany, Ialy, eherlands and Spain) for he selecion of he leading economic series. Their weigh, 89.4% of oal GDP in 2 2, is sufficienly represenaive. This paper is srucured as follows. Secion 2 presens a few conceps and he framewor of our wor. Secion 3 deals wih he efçi (984) mehodology and places i in relaion o Hamilon (989) Marov Swiching Model. Sec- * Prepared for he DIW Worshop on "Measuremen Problems of Business Cycles in he EMU", Berlin, 2 February 2. ** Cenre d Observaion Economique (27 avenue de Friedland, F Paris cedex 8) and Cenre d Economérie (Universiy Paris II-Panheon Assas). The views expressed in his paper are hose of he auhors and do no necessarily reflec he views of he Cenre d Observaion Economique from he Chamber of Commerce and Indusry of Paris. We are graeful o Lauren Ferrara and Paolo Guarda for heir helpful commens and o Anne de Guernon for her ranslaion and ediing suppor. Tel: ; Fax: ; This approach has been developed in he Cenre d Observaion Economique (COE) since 997 o build urning poin predicors for he growh cycles of France, Germany, Ialy, he Eurozone and he Unied Saes. See Anas (997) and guiffo-boyom (999) for deailed presenaions. 2 A curren prices and exchange raes (source: OECD). 364

2 ion 4 develops he COE leading indicaor (IARC) mehodology, wih special aenion o parameer esimaion and aggregaion procedure. Secion 5 presens he empirical resuls and reviews he forecasing performance of he IARC. 2. Turning Poin Deecion 2. The concep of urning poin Turning poins are evens which need o be defined (see Burns and Michell, 946; Oun, 96). Two main ypes of urning poins may be characerized (we shall focus on peas): Firs, he urning poin of he "classical" Business Cycle. I happens when he level of aciviy decreases sufficienly. 3 This downward phase of he Business Cycle is generally called a recession (or hard landing). Second, he urning poin of he Growh Cycle. I happens when he economic growh decreases below is rend growh rae 4 (he so-called sof landing). Someimes, he growh rae decreases bu remains above or close o he rend growh rae (very sof landing). In his case he economy slowdown is no sufficienly srong o impac on unemploymen for example. During he Asian crisis, he French and US economies were affeced in his way. Business cycles may become less frequen in he fuure or even disappear because moneary policy may have become more efficien and he mare raionally accouns for his regime shif. In any case, wha is imporan is o preven a sof landing from becoming a hard landing. As for he very sof landing, i has lile impac on he aggregae economy. In his paper we shall only focus on he urning poins of he growh cycle. 2.2 The European cycle: measuremen issues Few sudies (Aris and Zhang, 997 and 999) have ried o idenify he origins of a European Business or Growh Cycle. The creaion of he European Moneary Sysem (EMS) should have acceleraed he convergence of European economic cycles. However, in he 8 s, various asymmeric shocs weaened he correlaion beween he cycles in differen European counries. Saring wih he 993 recession, we have winessed a renewed increase in he correlaion beween European cycles as can be observed in figures and 2. 3 The rule of hree D s may be useful o idenify he recession: deepness, duraion and diffusion. 4 The growh cycle is, by definiion, equal o he deviaion of GDP from rend. Figure Euro-zone counries growh cycles: average, minimum and maximum 8 % of rend 6 Max Min Mean

3 Figure 2 2, Sandard deviaion in % Euro-zone counries growh cycles: sandard deviaion,5,,5, There are similariies wihin counry subgroups. The proximiy of German and Ialian cycles is well nown while he French cycle seems quie idiosyncraic in he region. Wih he creaion of he Euro in 999, he correlaion beween cycles has probably increased. everheless, he Asian shoc did no produce he same effecs on all counries. Germany and Ialy experienced a sof landing while France experienced a very sof landing. I is also ineresing o see how he deceleraing American economy will affec he differen Euro-zone counries. Eurosa calculaes he Euro-zone GDP. Various mehods are available o idenify he Euro-zone growh cycle. We chose he Band-Pass approach (Baxer-King filer, 995) o idenify he underlying rend. Unobserved Componens Models (Harvey, 985) may also provide urning poin idenificaion for boh shor and long erm cycles. Bu his breadown is more useful for ex-pos sudies han for predicions or real ime esimaion. Anoher class of idenificaion mehods involves regime swiching models wih fixed or variable ransiion probabiliies (Hamilonian models). Daing: Even ex-pos, he idenificaion of urning poins for business or growh cycles is no easy. Regarding he business cycles, he American BER daing commiee may wai unil one year o idenify he dae of he las recession. A grea number of series are analyzed for ha purpose. A common convenion is o idenify recessions as wo consecuive decreases in GDP quarerly growh. Anoher crierion for idenifying cycles includes he observaion crossing of he 5% hreshold in Hamilonian models. As ye, here is no commonly acceped crieria based on he movemen inensiy, he duraion and he evenual crossing of he rend for growh cycles. Forecasing: Very few urning poins forecass are available. A rule is needed o exrac he signal of a fuure cyclical urning poin from he leading indicaor (e. g. he Conference Board rule 5 ). Deecing: Deecing means looing for wha is hidden. In his case he urning poin has already occurred bu is no nown ye, because he series is no available or provisional and ofen volaile. Deecion is a real ime idenificaion of he urning poins. I is generally based on a coinciden indicaor. 2.3 Deecion Deecing cycle urning poins mus be disinguished from daing or forecasing hem. 5 Recession warnings are riggered when he annualised rae of change in he leading index falls below 3.5% while he diffusion index remains below 5% during a six-monh span. 366

4 efçi s formula is a useful ool for deecing swings in any variable. I also maes i possible o esimae he deecion delay. 2.4 Using efçi s formula o consruc a leading indicaor Our aim was o devise a leading indicaor of he growh cycle urning poins. The probabiliy of a urning poin of he reference series is based on he probabiliies of leading indicaors urning poins. An aggregaion mehod has been designed o consider boh ype I errors (ris of a false signal) and ype II errors (ris of missing he urning poin). We sill need o define a measure of he inensiy of a coming cyclical downurn. There are wo possibiliies. Eiher we ry o measure he movemen inensiy associaed wih he urning poin, or we will build a leading indicaor of Business Cycle urning poins. We are currenly woring on he second opion. In his approach, we focus on leading series crossing hresholds raher han on he deecion of peas and roughs. 3. efçi s Formula 3. The framewor The objecive is o predic cyclical urning poins, which mar he beginning or end of a cyclical downurn. For his purpose, efçi (982) developed a sochasic model for macroeconomic ime series. I is based on he assumpion ha he series behaves differenly depending on he downward or upward regime in which i evolves. Le us consider he sochasic process {X }, Z, where X represens observaions on incremens of he macroeconomic ime series considered. According o he finie sample (X ) =,...T we will infer he occurrence or non-occurrence of a change in he economic regime. Le Z (respecively Z ) be an ineger-valued random variable denoing he dae following a pea (respecively rough). 6 Le us suppose Z = i or Z = i which means ha a urning poin has appeared beween daes i and i. Wih he wo following assumpions, we will be able o characerize he cumulaive disribuion funcion: Assumpion : The probabiliy disribuion of {X i+j, j =,, 2, 3,...} is differen and independen of he disribuion of {X i j, j =,, 2, 3,...}. Assumpion 2: The observaions of X beween and wihin regimes are independen. If we consider ha a pea has appeared beween daes i and i, or in oher words {Z = i, i < }, hen: P(X x,..., X i x i,..., X x ) = F (x,..., x i ) F (x i,..., x ), where F (.) and F (.) are he wo cumulaive disribuion funcions for he upward and downward regime, respecively. 7 The variable Z is no direcly observable. Based on hisorical values of X we inend o deermine a any dae wheher a urning poin has already occurred (Z ) or no ye occurred (Z > ). Suppose ha he forecaser has gahered some experience from he sudy of pas urning poins and has subjecively defined a priori probabiliies. Le T be he a priori ransiion probabiliy of he change from upward o downward regime, T = P (Z = Z > ), and T he a priori probabiliy of he change from downward o upward regime T = P (Z = Z > ), Le us noe x = (x,..., x ) he hisorical values of X, since he las rough. Given x, le us evaluae a any dae he probabiliy of occurrence of a urning poin in he recen pas. Le P (P ) denoe he a poseriori probabiliy of occurrence of a pea (rough) a or before dae based on observaions of X : P P = P (Z x ). Using Bayes rule, we ge: P P ( x Z = and by exension P = P( x ) P ( Z P ( x ) P ( x Z ) P( Z ) Z ) P ( Z ) + P( x efçi s formula is recursively derived from (). For peas ( ): = 6 We suppose here ha Z refers o he dae of peas. The resuls are diamerally symmeric for roughs. Z refers o he dae of roughs. 7 We adop here he convenional noaion for discree values variables: capial leers for random variabls and small leers for paricular realisaions., ) Z > ) P ( Z () > ) (2) [ P + ( P ) T ] f ( x ) [ P + ( P ) T ] f ( x ) + [( P )( T )] f ( x ) 367

5 where ƒ (.) is he densiy funcion of X during a downward regime and ƒ (.) during an upward regime, and where P =. We see from formula (2) ha efçi s formula allows us o compue he a poseriori probabiliy of occurrence of a urning poin, incorporaing curren informaion ino he poserior probabiliies esimaed over previous periods. As described in iemira (99): "[...] he efçi mehod accumulaes probabiliies from he sar of he previous urning poin. This paricular dynamic characerisic of he efçi mehod is a major improvemen over is predecessors." This is an advanage over he Probi approach which has a poor dynamic conens and may herefore be less powerful if he lead imes are unsable. The efçi s model appears o be a special case of he regime swiching approach developed by Hamilon (989) in which he observed X are assumed o depend on wo differen unobservable saes. 8 Suppose S = sands for he downward regime and S = sands for he upward regime. By comparison wih efçi s noaion: P = P (Z x ) = P (S = x ) The underlying efçi s model can be wrien as:, X = a + a S + ε, (3) where: ε ~ iid (, σ + σ S ). Assuming a ormal disribuion for ε we ge: X ~ (a + a S,σ + σ S ). The Transiion probabiliies are indicaive of he persisence of he process. Hamilon (989) assumed ha hese probabiliies are consan over ime. However recen wors (see, for insance, Filardo, 994) propose ime dependen ransiion probabiliies as a funcion of he age of he phase, or based on a leading indicaor. In efçi s approach, he ransiion probabiliies are also non-consan and are esimaed from pas experience. Assume ha {Y } is a sochasic process where Y represens observaions on incremens of a macroeconomic coinciden variable (GDP) and assume ha {X } is a leading index. The underlying idea is ha evens saring a downurn in Y will be presen in {X } before hey show up in {Y }. We need o inroduce a decision rule so as o signal he forhcoming urning poin in he macroeconomics coinciden ime series. For his reason, we have o define a criical value for probabiliies o minimize ype I errors. Le θ be he hreshold beyond which we consider ha a urning poin has appeared in X. efçi (982) calls θ he probabiliy of a false alarm, while iemira (99) defines θ as he confidence level. 3.2 Parameers esimaion The parameers of he probabiliy disribuion funcion of X are esimaed over samples made up of upward and downward regimes. The a priori ransiion probabiliies denoed T and T mus also be esimaed. The firs sep consiss in an a priori daing of he peas and roughs of he growh cycle of X. The daa are spli ino upward and downward regimes in order o obain wo separae samples composed respecively of observaions belonging o upward and downward regimes. The parameers of he probabiliy densiy funcions (ƒ (X ) and ƒ (X )) and he a priori probabiliies (T and T ) are compued dynamically. A few assumpions are needed o esimae he parameers. We may suppose ha he probabiliy of a urning poin is an increasing funcion of he age of he regime. In his case a priori ransiion probabiliies are duraion dependen. Oherwise hey will be consan. The probabiliy densiy funcions are esimaed using an empirical disribuion of X or by fiing a abulae densiy funcion o observaions of X in each regime. The hreshold θ has o be se o define he decision rule: a signal of imminen cyclical urning poin is given when he probabiliy P or P reaches θ. We define he deecion delay as he ime necessary o deec a urning poin. This delay depends on he value of θ, whose choice also represens a compromise beween he cos of a false signal and he cos of a oo lae signal. P (P ) is iniialized o for he firs observaion, and more generally when a downward (upward) regime ends. efçi (982) uses he U.S. Deparmen of Commerce s composie index of leading indicaors o es he recursive formula and o see if i could have prediced he 974 recession and he 979 slowdown. Parameers are esimaed over he period and sequenial probabiliies calculaed from 97. The densiy funcions ƒ (X ) and ƒ (X ) are esimaed by using he empirical frequency disribuion of X during upward and downward periods. A priori ransiion probabiliies are approximaed using a symmeric densiy wih a mean of 5 monhs because of he duraion dependence assumpion. The θ value is se a.. Finally, efçi concludes ha his decision rule is opimal o predic cyclical downurns. Oher empirical sudies combine alernaive assumpions as in Diebold and Rudebusch (989), iemira (99) 8 A main difference however is ha under he Hamilon s model, regimes are always oally unnown (hidden process) while hey are supposed nown a leas in he pas under efçi s approach. 368

6 and Aris e al. (995), or use moneary and financial variables as leading indicaors as in Palash and Radeci (985). Therefore efçi s approach has mainly been used o assess he relevance of signals obained from a leading composie index. In oher words, he sequenial formula is a way o exrac probabilisic signals from composie indices ha are oherwise difficul o inerpre. The nex secion provides an original applicaion of efçi s formula o build a cyclical urning poin leading indicaor called IARC 9 from he French acronym. This one is produced monhly and published by he COE for France, Germany, Ialy, he Euro-zone and he Unies Saes. 4. The COE Leading Indicaor 4. The COE approach Classical leading composie indices are ofen consruced as a weighed average of normalized leading indicaors. The rule for inerpreing hese composie indices (paricularly o idenify a signal) is eiher absen (OECD) or ad hoc (Conference Board). The efçi s formula may be used o exrac he signal of hose composie indices (Aris e al.,995; Diebold and Rudebusch,989). Our approach is differen. We sar wih he idea ha he combinaion of saisical informaion is easier o perform in he space of probabiliies han in he space of ime series. Time series are ofen difficul o compare because of heir differen naure: opinion surveys or values, raes or levels, differen frequencies and volailiies. We herefore prefer o compue he probabiliy of a fuure signal by using a se of leading indicaors and find a way o aggregae he probabiliies of heir signals. Firs of all, we need o selec a se of leading indicaors by evaluaing heir performance. The operaional lead is defined as he heoreical lead minus he deecion delay and he availabiliy delay: OL = TL DD AD, where OL represens he operaional lead, TL he heoreical lead, DD he deecion delay and AD he availabiliy delay. The heoreical lead refers o he average observed lead beween he urning poin of he leading indicaor and he corresponding coinciden cyclical urning poin. A subsanial heoreical lead would no be useful if, a he same ime, he deecion delay were oo long. For insance, we had o give up he boxboard new orders series radiionally considered as a leading series in France because he series urned ou o be oo volaile, implying a long deecion delay. Since we aim a forecasing he growh cycle urning poins, we exraced he rend componen of each nonsaionary series by using he Hodric-Presco filer (more sensiive o a change of direcion han he Baxer- King filer). To apply he efçi formula we previously fied a ormal densiy funcion o esimae ƒ (X ) and ƒ (X ). iemira (99) cies McCulloch (975): "[...] once an expansion or recession has exceeded is hisorical minimum duraion, he probabiliy of a urning poin is independen of is age. Therefore, a simple sraegy would be o have probabiliies buil o he average duraion and hen held consan. " We have used his "simple sraegy" o esimae he a priori ransiion probabiliies in a saic way because he efçi formula does no appear o be sensiive o a change in he esimaion of T and T. Generally he esimae for monhly series is close o 5% which ranslaes in an average consan duraion of beween.5 and 2 years. As in Aris e al. (995), he value of θ has been fixed o.5. A false signal is a signal of a leading indicaor wihou any coinciden cyclical urning poin wihin a predefined horizon. The false signal is wha we will call he ype I error. The oher ris is o miss he coinciden urning poin, which we will call he ype II error. 4.2 The aggregaion procedure We aim o aggregae he a poseriori probabiliies obained for each leading indicaor from formula (2) and (3). Suppose we seleced leading indicaors X, =, 2,.... For each of he leading X, we associae a laen variable X ~ ha equals if a urning poin of he series X has occurred before and oherwise. We define P = P(X ~ = ) as he efçi sequenial probabiliy of a recen urning poin (assume i is a pea) of he h he leading indicaor. The quesion now is how o aggregae he probabiliies P. A firs mehodology would be a generalizaion of he diffusion index approach. The formula of he diffusion index when searching for a pea is: I () = X ~ This diffusion index represens he percenage of leading indicaors, which have reached a pea. In pracice, a good way o measure his is o compue he change over a six-monh span. The decision rule is 9 In French, Indicaeur Avancé de Reournemen Conjoncurel (Leading Indicaor of Cyclical Turning Poins). Also disseminaed regularly on he COE websie: ccip.fr. This diffusion index is used by he Conference Board as a way o esimae he exen of breadh of a paricular cyclical movemen. 369

7 o deec when his change becomes negaive. The formula becomes ( ) = I 2 ( X < X 6 ) We observe ha each series in his index has he same weigh. We consider ha he mahemaical expecaion of he diffusion index is a beer esimae: E [ I ) ] = E[ ~ ] ( ( X = ) = P = We call his index he sequenial probabiliies diffusion index. A shorcoming of his approach is o ignore he possible correlaion beween he sequenial probabiliies. We implicily give he same weigh o each leading indicaor, which does no seem correc. Looing more closely o our goal (anicipaing he peas and roughs of he global economy), we inroduce an implici weighing scheme: Consider a given forecas horizon H and define he random variable R equal o if a cyclical urning poin of he global economy occurs beween and + H and oherwise. For each leading indicaor X he probabiliy of an upcoming cyclical urning poin can be developed by using he Bayesian formula as follows: P(R = ) = P (R = X ~ = ) P (X ~ = ) + P (R = X ~ = ) P (X ~ = ) The wo riss 2 associaed wih his approach are: Firs, he ris of a false signal (or ype I error) α, such as: α = P (R = X ~ = ), Second, he ris of missing he cyclical urning poin 3 (or second ype error) β, such as: β = P (R = X ~ = ), Boh riss are assumed o be consan over ime, i. e.:, α = α and β = β P ~ ( X = ) (4) oe ha P (R = ) may reach only if α =, ha is if he leading indicaor did no produce any false signal in he pas. oe also ha P (R = ) has a minimum value of β which represens he probabiliy of missing a cyclical urning poin. In pracice, for any H, esimaion of α and β is done over he pas by confroning he chronology of leading indicaor signals wih he coinciden cyclical daing. The probabiliy of he ype I error is he raio of he number of false signals o he oal number of leading indicaor urning poins, while he probabiliy of he ype II error is he raio of he number of missed urning poins o he oal number of coinciden cyclical urning poins. The Bayesian formula (5) can be generalized o leading indicaors bu his mulivariae formula becomes very complex and implies he esimaion of oo many parameers. However, i would be an effecive way o ae ino accoun he correlaions beween leading indicaors. The idea is o consider ha we have univariae esimaes of P(R = ). We can use a Probi approach o find he bes weighed linear combinaion of hose probabiliies. However, his alernaive resuls in non-significan coefficiens a he % hreshold. As a generalizaion of he diffusion index and considering we have a sample {P (R = )} of esimaes of P(R = ), we have decided o use a simple average of hose esimaes: P ( R = ) = = = [ ] β + ( α β ) P (6) = _ β + ( α β ) P (7) = Thus defined, his aggregaion can be seen as he average of a poseriori probabiliies weighed by he probabiliies of ype I and ype II errors. This formula has he advanage o be easily inerpreable: values vary inside an inerval which bounds are defined by he average probabiliies of ype I and ype II errors: [β, α ]; he inferior bound is reached if all a poseriori probabiliies equal and he superior bound if all a poseriori probabiliies equal. The drawbac of his formula is ha he higher he average probabiliy of ype I error, he smaller he upper bound. Hence inerpreaion becomes more difficul, noably for cross-counry comparisons. For his reason, we decided o normalize his formula by dividing i by ( α ) so ha i would equal as soon as a poseriori probabiliies equal. The final index we use (ha we call IARC) is An esimae of P(R = ) is P (R = ) defined by: P (R = ) = ( α ) P + β ( P ) = β + ( α β )P. (5) 2 The wo riss are discussed a large in he seminal aricle of Oun (96). 3 Eiher because he leading indicaor missed he general economic urning poin or because he signal was oo lae. 37

8 IARC β = α + ( ) = α β ( α ) = P The las sep consiss in choosing a reading mehod in order o inerpre movemens of he IARC index. ow ha he a poseriori probabiliies have been aggregaed, a hreshold for he index IARC has o be defined. We decided o ae wo empirically esimaed hresholds ino accoun over he period They are a way o mae he undersanding of he signal easier because we feel ha a rough probabiliy would be oo difficul o inerpre. The 6% hreshold corresponds o abou 7% chances of a rue signal and he 8% hreshold is clearly a srong signal which can be inerpreed as: "we forecas a urning poin". A urning poin may occur in he nex nine monhs when he IARC index reaches 6%. A urning poin will probably occur in he nex hree monhs when he IARC index reaches 8%. (8) Toal GDP for he Euro-zone 4 (see series in he appendix) was used as a basis o evaluae he growh cycle. Daing was based on hree growh cycle esimaes derived from he Hodric-Presco filer (HP filer), he Baxer-King band-pass filer (BP filer) and an Unobserved Componens Model (UCM). The las model is used in a simple univariae way, 5 wih a slowly moving smooh rend specificaion assuming he combinaion of a shor and long-erm cycle (periodiciy of 3 and 2 years respecively): Log (GDP) = T + C + ε T = T + β β = β + ξ where T, C and ε represens respecively he rend, cyclical and irregular componens. The daaion was based mainly on he peas and roughs of he Baxer-King filer resuls. 5. Applicaion o he Euro-zone 5. Daing he growh cycle 4 Index base = 995 Q. Eurosa daa since 995 Q and exrapolaed bacwards o 97 by he auhors for all Eurozone counries, excep Greece, Irland and Luxembourg (naional volume indices are weighed by nominal GDP a prices and curren PPP s of 995, according o OECD publicaion, 999). 5 More sophisicaed bivariae or mulivariae models may improve he esimaion. Figure 3 Euro-zone GDP: growh cycle BP filer HP filer UCM

9 Table Daing of Eurozone growh cycle Cycle Pea Trough Pea Slowdown Expansion Cycle Duraion in monhs ov. 73 Aug. 75 ov ov. 76 ov. 77 Dec Dec. 79 Jan. 83 Oc Oc. 85 Apr. 87 ov ov. 9 Aug. 93 Feb Feb. 95 ov. 96 Feb Feb. 98 June 99 ov Mean Selecion of leading indicaors Each leading indicaor for he Euro-zone is a weighed average of member counries leading indicaors. 6 We seleced five leading indicaors 7 : a soc mare index, he spread beween long and shor erm ineres raes, he firs facor of a principal componen analysis of business survey resuls in he inermediae goods indusry, manufacurer prices expecaions concerning wholesale rade and he COE leading indicaor of he American growh cycle (cf. figure 4). For each series, a calculaion of he operaional mean lead is performed over he period. The 8 s do no provide a good period for esimaing he performance of indicaors due o he relaive heerogeneiy of economic growh cycles in he zone. Crieria used for selecing he indicaors are numerous. As oulined by he OECD, an economic raionale is needed o avoid aing only he saisical performance on a period of ime ino accoun. Also he series need o be available for a long period of ime o allow for esimaion. Bu he main selecion crieria relaes o he degree and sabiliy of he operaional lead as well as he low degree of firs and second ype riss. There is generally a rade-off: when he lead increases, he riss increase a he same ime. Tables 2 (lead if negaive, lag if posiive) and 3 show he good predicive performance of he financial indicaors: he soc index and he ineres rae spread. The probabiliies of ype I and ype II errors in able 3 are raher low. 6 The weighs are relaed o he value of GP expressed in purchasing power pariy. For he year 995, he weighs are 33.2% for Germany, 23.% for France, 22.2% for Ialy,.% for Spain, 6.% for he eherlands and 4.3% for Belgium. Observe ha only large counries have been used as a firs proxy. 7 See he lis of series and sources in Appendix "Lis of ime series and sources". Table 3 Type I and ype II errors α Euro-Soc.25.6 Euro-Spread.6 β Table 2 GDP daaion Theoriical lead, deecion delay and operaional lead Euro-Soc Euro-Spread TL DD ) OL TL DD ) OL Peas ov Feb Feb ov Throughs Aug ov June ) Esimaed by efçi s formula. 372

10 Figure 4 Componens of he leading indicaor for he Euro-zone We observe wo false signals relaed o he Euro-Soc in June 99 for he pea and in December 99 for he rough. 2 Percen Soc mare index 5.3 Performance Percen Ineres spread As shown in he following graphics, a srong signal is always emied in he 3 monhs preceding he urning poin. I seems very probable ha he Euro-zone upward growh cycle phase ended in he las quarer of 2. A srong signal was given by he COE leading indicaor in Ocober 2, anicipaing a pea in he hree following monhs (cf. figure 6). This was quie a good performance since a ha ime mos economiss were raher opimisic abou economic growh in 2 and did no anicipae any pea in he growh cycle. The COE indicaor is now used o anicipae he nex rough. The curren level ( in March 2) of he indicaor does no allow o forecas any exi from he curren slowdown during he following nine monhs (cf. figure 7) , -, -2, Percen Leading indicaor for USA growh cycle Indusrial survey (inermediae goods secor) Price prospecs on inermediae goods Implicaion of he signal When he pea is confirmed, i means ha he Euro-zone growh rae decreases below is rend growh rae. If we consider he Baxer-King filer resuls, a 2.5% rend growh rae was esimaed a he end of 2. A Probi analysis also esimaes he hreshold a 2.4%. If we regress he annual change of quarerly GDP on recession phases, he bes model is obained wih a lead of one or wo quarers. If we regress he quarerly change, he bes model is obained wih a cenered 3 quarers moving average wihou delay. Consequenly, we have o wai 4 o 5 monhs o chec wheher his implicaion has maerialized. 5.5 Conclusion In his paper, we showed ha efçi s crierion may be a useful way o selec leading economic ime series and o predic cyclical urning poins of he Euro-zone in paricular. However, assumpions are crucial and would need more invesigaion lie duraion dependence and asymmery ess. Also, i could be beneficial o ae he correlaion beween and wihin economic series ino accoun. Finally, a business cycle leading indicaor needs o be elaboraed in order o inform on he inensiy of a coming slowdown signaled by he growh cycle leading indicaor. Recession Slowdown 8 The index varies from o when searching for a rough (wih hresholds of 6 and 8). 373

11 Figure 5 Performance of he Euro-zone leading indicaor Leading indicaor of urning poins 995/2 998/ Expansion Slowdown March / / 999/5 - Srong probabiliy of urning poin (nex 3 monhs) Possibiliy of urning poin (nex 9 monhs) % GDP (on he lef) GDP and indusrial producion Trend deviaion (Baxer King filer) indusrial producion (on he righ) Q Q2 Q3 Q4 Q Q2 Q3 Q4 Q Q2 Q3 Q4 Q Q2 Q3 Q4 Q Q2 Q3 Q4 Q Q2 Q3 Q4 Q Q2 Q3 Q4 Q Q2 Q3 Q4 Q Q2 Q3 Q4 Q Q2 Q Recession Slowdown References Anas, J. (999): Le cycle économique européen: daaion e déecion. In: Les muaions de l économie mondiale. Chambre de Commerce e d Indusrie de Paris sous la direcion de Chrisian de Boissieu. In: Economica, Anas, J. (997): Forecasing Turning Poins of he French Growh Cycle. 22h Cire Conference. Helsini, Finland. Aris, M. J., R. C. Bladen-Hovell, D. R. Osborn, G. Smih and W. Zhang (995): Turning poin predicion for he UK using CSO leading Indicaors. In: Oxford Economic Paper, Vol. 47. Aris, M. J., and W. Zhang (997): Inernaional Business Cycles and he ERM: Is here a European Business Cycle? In: Inernaional Journal of Finance and Economics, 2 (),

12 Figure IARC Eurozone (Search of nex pea) ov Aris, M. J., and W. Zhang (999): Furher Evidence on he Inernaional Business Cycles and he ERM: Is here a European Business Cycle? In: Oxford Economic Paper, 5, Baxer, M., and R. King (995): Measuring Business Cycles: Approximae Band-Pass Filers for Economic Time Series. In: BER Woring Paper, o Burns, A. F., and W. C. Michell (946): Measuring Business Cycles. In: BER Sudies in Business Cycles, o. 2. Columbia Universiy Press, ew Yor. Diebold, F. X., and G. D. Rudebush (987): Scoring he Leading Indicaors. In: Special Sudies Paper, o. 26. Federal Reserve Board, Washingon, D. C. Filardo, A. J. (994): Business-Cycles Phases and Their Transiional Dynamics. In: Journal of Business and Economic Saisics, 2 (3), A S O D J F M A M J J A S O Srong probabiliy of downurn Possibiliy of downurn Hamilon (989): A ew Approach o he Economic Analysis of on-saionary Time Series and he Business Cycles. In: Economerica, 57 (2), Harvey, A. C. (985): Trend and Cycles in Macroeconomic Times Series. In: Journal of Business and Economic Saisics, 3 (3), Mcculloch, J. H. (975): The Mone Carlo Cycle in Business Aciviy. In: Economic Inquiry, 3, Figure 7 IARC Eurozone (Search of nex rough) efçi, S.. (982): Opimal Predicion of Cyclical Downurns. In: Journal of Economic Dynamics and Conrol, 4, March guiffo-boyom, M. (999): L Indicaeur Avancé de Reournemen Conjoncurel Européen. Technical Paper 34, Cenre d Observaion Economique. iemira, M. P. (99): An inernaional applicaion of efçi s probabiliy approach for signaling growh recessions and recoveries using urning poin indicaors. In: K. Lahiri and G. H. Moore (eds): Leading Economic Indicaors: ew Approaches and Forecasing Records. Cambridge Universiy Press, 9 8. Oun, A. M. (96): On he Appraisal of Cyclical Turning- Poin Predicors. In: Journal of Business of he Universiy of Chicago, 33 (2). - D J F M A M J J A S O 2 2 D Palash, C. J., and L. J. Radeci (985): Using Moneary and Financial Variables o Predic Cyclical Downurns. In: Quarerly Review of he Federal Reserve Board of ew Yor, Summer. Possibiliy of upurn Srong probabiliy of upurn 375

13 Appendix Lis of ime series and sources ame Counry Periodiciy Delay Source Shor-erm Eurozone monhly 4 days hree-monh Euribor ineres rae Long-erm France monhly 2 days public secor bonds (Banque de France) ineres rae Long-erm Germany monhly 4 days governmen bonds (Bundesban) ineres rae Soc mare Germany monhly 3 days Francfor index FAZ indices Belgium monhly 3 days Brussels general index Spain monhly 3 days Madrid index Ialy monhly 3 days Indice generale de la Banca commerciale ialiana eherlands monhly 3 days Amserdam general index France monhly 3 days Index SBF25 Indusrial survey Eurozone monhly 2 days European Commission (EEC-ECF) in inermediae goods secor Expeced prices on Germany monhly 25 days IFO Business Survey: wholesale rade price anicipaion for inerinermediae goods mediae and invesmen goods [Wes Germany]) Ialy monhly monh ISAE Business Survey: selling price forecas in inermediae + 3 days goods secor France bimonhly days ISEE wholesale rade survey every 2 Wholesale rade survey: price 3 o 4 monhs expecaion in indusmonhs rial inermediae goods secors Leading index for USA monhly 5 days COE USA growh cycle Zusammenfassung Ein neuer Indiaor auf Basis des Ansazes von efçi zur Vorhersage der Wendepune in Wachsumszylen Der Aufsaz greif die Idee auf, dass in vielen Siuaionen Enscheidungen nich sofor geroffen werden müssen, sondern verschoben werden, bis zusäzliche Informaionen zur Verfügung sehen. Sequenielle Analysemehoden scheinen daher für das Problem der Wendepunanalyse besonders geeigne zu sein. Hierfür wird auf den Ansaz von efçi zurücgreifend ein Wahrscheinlicheisindiaor für ünfige Wendepune des europäischen Konjunurzylus vorgesell. 376