Business cycle correlation of the CEEC and the Euro area: some methodological controversy Ladislava Grochová 1, Petr Rozmahel 2

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1 Business cycle correlaion of he CEEC and he Euro area: some mehodological conroversy Ladislava Grochová, Per Rozmahel 2 Inroducion Absrac. The paper focuses on some mehodological feaures of he business cycle correlaion measuring. Paricularly, a spurious influence of derending echniques used when analyzing he classical and growh business cycles is examined in he paper. The resuls give some evidence of differen impac of derending filers on final measures of correlaion since uneven volailiy, auocorrelaion and oher characerisics in derended ime series are produced by he filering echniques. This migh lead o a biased or disored inerpreaion of he resuls when assessing business cycle correlaion. Keywords: business cycle, correlaion, derending, Hodrick-Presco filer, bandpass filer, JEL Classificaion: C8, C82, E32 AMS Classificaion: 9G70 During pas wo decades a vas variey of research papers and analyical sudies on business cycle similariy measuring were published in economic lieraure. The business cycle similariy and convergence was assessed mainly wih regards o analyzing he economic and moneary inegraion processes in Europe. Paricularly, business cycles of candidae counries aceeding he Euro zone were analyzed and compared wih he member counries cycles. The characerisic of business cycle similariy and shock asymmery were defined in a frame on he New Opimum Currency Areas Theory [0]. Technically, he classical and growh business cycles have o be idenified firs in order o apply some measure of similariy. Burns and Michell [2] define he classical business cycles as cyclical flucuaions wih decline and growh phases in an absolue level of aggregae economic aciviy of a naion. The growh cycles are considered as flucuaions of cyclical componen of analyzed macroeconomic ime series around is rend [9]. Accordingly, a seleced derending echnique o dissec he cycles and rends in he daa ime series need o be applied. The OCA lieraure provides a general heoreical framework for business cycle similariy assessmen []. However, he heory does no give a clear recommendaion of a concree mehod or echnique o be applied. Thus a vas variey of derending and cycle idenificaion mehod was used in he pas lieraure. Fidrmuc and Korhonen [7] used a mea-analysis of he business cycle correlaion beween he Euro area and Cenral and Easern European counries (CEEC) analyzing 35 seleced publicaions on business cycle synchronizaion in Europe. In he analysis hey compare he daases, mehods including derending echniques and resuls of chosen opical papers. Among ohers hey found more conservaive and careful esimaion resuls in sudies by he cenral banks comparing o hose by research insiuions and academia. There is also a lo of economeric and saisical lieraure dealing wih impac of using mehods such as filers on resuled ime series including business cycles (e.g. [], [4], [5], [3], [2], [6], and [4]) In our paper we concenrae on he role of derending echniques and filers in he business cycle correlaion analysis. Paricularly, we focus on evaluaion of spurious impacs of various derending echniques on macroeconomic ime series when esimaing he business cycles correlaion. The paper is srucured as follows. Afer he inroducion he second session describes he daa and used mehodology. The correlaion of business cycles and derended ime series characerisics are compared in he hird secion. The fourh secion concludes. 2 Daa and mehodology The monhly daa of indusrial producion in sourced from IFS IMF is used when analyzing he business cycles. Germany, France, Ialy, Spain and Porugal were seleced as he represenaives of core and peripheral Euro area counries. Czech Republic, Hungary, Poland and Slovakia complee he sample of CEE counries. Mendel Universiy in Brno, deparmen of Economics, Zemědělská, Brno, Czech Republic, ladislava.grochova[a]mendelu.cz. 2 Mendel Universiy in Brno, deparmen of Economics, Zemědělská, Brno, Czech Republic, per.rozmahel[a]mendelu.cz

2 The Hodrick-Presco filer, Baxer-King band pass filer using for idenificaion of growh cycles and firs differencing of logarihms for classical cycles were applied in he analysis. There is a lack of consensus in economic lieraure for he classical business cycles idenificaion. The firs differencing mehod is used in sudies on classical as well as growh cycle. As Canova [5] poins ou he firs differencing of logarihms is an appropriae mehod producing saionary ime series provided ha he rend componen represens he random walk process, cyclical componen is saionary and boh componens are no correlaed. In addiion he uni roo of y is supposed due o sysemaic componen y -, for y = + ε () y For which a rend is defined as g = y and c = y y. ˆ The Hoddrick-Presco filer [8] enables o dissec he sochasic rend and uncorrelaed cyclical componen in analyzed ime series solving he minimum problem T T 2 + c λ = = = min T { g } 2 [( g g ) ( g g )], λ > 0 + (2) We apply he smoohing parameer λ=4400 (monhly daa) penalizing he variabiliy in he growh componen. The value of smoohing parameer λ can be adjused according o he business cycle definiion. The greaer λ he smooher rend idenified in he ime series. Finally he frequency domain band pass filer suggesed by Baxer and King [] was applied in he paper. The assumpion drawn from Burns-Michell [2] of he suggesed filer is he cycle no shorer han.5 year and no longer han 8 years. The Baxer-King filer is basically he wo-sided symmeric linear filer in a form of a combinaion of low-pass ad high pass filer passing by he componens wih periodical flucuaions beween 6-32 quarers of he specrum. The componens wih flucuaions of higher or lower frequencies are removed by he filer. The auhors define he ideal runcaion period K=2 for quarerly daa and K=36 for monhly daa. This implies eliminaing of 2 and 36 observaions, respecively, a he beginning and he end of he ime series [3]. The lengh of he runcaion period improves he equaliy of resuling ime series decomposiion bu bigger loss of daa. Concerning he mehods used he cross-correlaion analysis of analyzed counries is applied firs. The resulan correlaion marices are compared in case of all hree derending echniques applied in order o poin ou significan differences in resulan correlaion coefficiens when using various filers. Nex, he business cycle of seleced counry idenified wih seleced derending echniques is described and characerized. Finally, he resulan derended ime series approximaing he business cycles are analyzed and compared focusing on filers properies such as auocorrelaion, sandard deviaion and a frequency of urning poins in order o examine various effecs of seleced derending echniques. 3 Business cycle correlaion of CEEC and he Euro area 3. Cross correlaion Table includes he cross correlaion coefficiens wih p-values of all seleced counries. The coefficiens resuled from using he Hedrick-Presco (HP) and Baxer-King band pass filer (BK) are compared in a cross correlaion marix. Table 2 complees he resuls obained wih applying he firs differencing echnique. bk_fr bk_i bk_de bk_es bk_pl bk_hu bk_cz bk_sk hp_fr bk_fr hp_i bk_i hp_de bk_de hp_es bk_es

3 hp_pl bk_pl hp_hu bk_hu hp_cz bk_cz hp_sk bk_sk hp_fr hp_i hp_de hp_es hp_pl hp_hu hp_cz hp_sk Table Saisical characerisics of indusrial producion cycles idenified wih Hodrick-Presco and Baxer- King band pass filer; source: auhor s calculaions; p-values in parenheses, fd_fr fd_fr fd_i fd_de fd_es fd_pl fd_hu fd_cz fd_sk fd_i (0.0000) fd_de (0.0000) (0.0000) fd_es (0.0000) (0.0000) (0,003) fd_pl (0.000) (0.003) (0.2080) (0.002) fd_hu (0.003) (0.074) (0.0007) (0.0069) (0.0870) fd_cz (0.007) (0.0004) (0.0672) (0.0065) (0.0000) (0.000) fd_sk (0.00) (0.007) (0.0437) (0.077) (0.0000) (0.0588) (0.0000) Table 2 Saisical characerisics of indusrial producion cycles idenified wih firs differencing; source: auhor s calculaions; p-values in parenheses. Comparing he resuls in boh ables one migh conclude ha he Euro zone member counries reveal higher cross correlaion han he CEE counries. Using he HP filer all counries seem o share a kind of European business cycle since all correlaion coefficiens higher han 0.5 wih high saisical significance. Even he CEE counries such as he Czech Republic and Hungary show business cycles highly correlaed o Germany as a benchmark for he Euro zone average. Resuls in case of using he BK filer are very similar o hose of HP filer. Apar from few excepions he cross correlaion confirms highly similar cycles in he whole analyzed period of However, he siuaion is dramaically differen in case of applying he firs differencing echnique. All cross correlaion coefficiens are significanly lower han hose of using HP and BK filers. The resulan coefficiens even give an evidence of uncorrelaed cycles wih high saisical significance. Le s recall ha firs differencing of logarihm of he macroeconomic daa implies an approximaion of he growh raes, which is commonly used in sudies on economic inegraion. Since he underlying OCA heory does no provide a clear mehodological recommendaion on a concree business cycle idenificaion mehod, he researchers differ in choosing he derending echniques, which migh influence he final correlaion resuls. Accordingly, he final inerpreaion of numerical resuls such as business cycle correlaion migh be spurious wihou consideraion of differen mehodological properies

4 3.2 Derending echniques influence To shed some ligh on he raionale of a significanly differen correlaion resuls obained when using various filers we now focus on seleced saisical properies of applied derending echniques. The Figure shows he derended ime series when using firs differencing, Hodrick-Presco and Baxer-King filers. The firs differencing echnique produces cycles of lower volaile ime series measured wih sandard deviaion and more frequen urning poins. HP and BK filers generae raher smooher cycles. This is more obvious when using quarerly daa of GDP which has less srengh in he higher frequencies of he specra. In our paper we use monhly daa of indusrial producion, which produce frequen urning poins in he derended ime series. Figure Firs differencing, Hodrick-Presco and Baxer-King filers comparison: he case of Czech indusrial producion cycles Variable Obs Mean Sd. Dev. Min Max r() r(2) r(3) Turning Poins hp_fr hp_i hp_de hp_es hp_pl hp_hu hp_cz hp_sk fd_fr E fd_i fd_de fd_es fd_pl fd_hu

5 fd_cz fd_sk bk_fr bk_i bk_de bk_es bk_pl bk_hu bk_cz bk_sk Table 3 Saisical characerisics of indusrial producion cycles idenified wih he chosen echniques, source: auhor s calculaions The able 3 summarizes seleced properies of derended ime series of monhly indusrial producion in The analyzed ime series is six years shorer since he Baxer-King band pass filer needs hree years (runcaion period) o be cu off a he beginning and he end of he analysed ime period. The analyzed properies include seleced descripive saisics, auocorrelaion measures and also number of urning poins a he derended ime series. The monhly daa of indusrial producion does no allow deecing he lowes sandard deviaion in case of firs differencing as suggesed in Baxer-King []. The measures of auocorrelaion and number of urning poins provide evidence of differen properies of seleced filers. The Hodrick-Presco and Baxer- King band pass filer reveal remarkably higher correlaion han firs differencing echnique. In addiion, he number of urning poins is 3-5 imes higher when using firs differencing hen HP and BK filers. On he conrary HP and BK filers produce ime series wih very comparable number of urning poins. As suggesed in Baxer-King [] firs differencing emphasises high frequencies and down weighs low frequencies of he ime series specra. This implies lower correlaion and auocorrelaion in derended ime series when using firs differencing. HP and BK filers work as band pass filers. HP filer acs as a high-pass filer which leaves componens of higher frequencies in he ime series whereas he BK-BP removes hem. The correlaion and auocorrelaion measures are higher when using quarerly and monhly daa of GDP and oher aggregae aciviy indicaors ha do no have much of high frequencies in he specra. Also volailiy measured wih sandard deviaion is higher han in case of firs differencing in case of quarerly daa. Using monhly daa of indusrial producion our resuls confirm hose of Baxer-King []. Sandard deviaion of cycles when using firs differencing is no significanly lower han of he oher filers. This migh be he impac of using monhly daa since Baxer-King [] also found comparable sandard deviaions in ime series when using monhly daa of inflaion rae and oher seleced indicaors. 4 Conclusion In our paper we inended o provide some evidence of an influence of seleced derending echniques on business cycle correlaion measuring. Three seleced derending echniques were applied o idenify cycles of monhly indusrial producion in seleced EU counries including he CEEC. The resuls of business cycles cross correlaion show significan differences when using band pass filers and firs differencing. Whereas business cycle correlaion idenified wih using Hodrick-Presco and Baxer-King band pas filers are highly correlaed, cycles derended wih firs differencing are uncorrelaed. This migh imply spurious inerpreaion when assessing he business cycle similariy from OCA heory perspecive. Analysis of seleced saisical properies of filered ime series show significan differences in measures of auocorrelaion and number of urning poins. Firs differencing produce ime series wih low auocorrelaion and highly frequened urning poins. Band pass filers produce raher smooher cycles in erms of significanly lower number of urning poins and higher auocorrelaion measures. All hree filers emphasize and down weigh dissimilar frequencies of he ime series specra. The resuls also indicae poenially differen properies of filering echniques when using quarerly and monhly daa. Since here is a lack of consensus on business cycle idenificaion echnique in he lieraure, he assessmen of business cycle similariy migh lead o inappropriae inerpreaion due o uneven impac of chosen filers. Accordingly, our recommendaions are aimed a careful inerpreaion of resuls wih respec o applied mehodology

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