Okun s Coefficient for four Mediterranean member. countries of EU: An empirical study

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1 Okun s Coefficien for four Medierranean member counries of EU: An empirical sudy Absrac Chaido Drisaki and Nikolaos Drisakis Universiy of Macedonia 56 Egnaia sr, P.O Box Thessaloniki Greece Tel: drisaki@uom.gr, dris@uom.gr In his paper, we esimae Okun s coefficiens for four Medierranean counries of EU using real GDP and unemploymen rae daa. For he empirical analysis of he research we used annual daa for he period and odrick and Presco filer (997), a mahemaical ool used in macroeconomics and especially in business cycles heory, in order o find ficiious daa using variaion and correlaion for boh variables. Research resuls showed ha unemploymen cos, from he real GDP loss viewpoin, is larger for Ialy (-0.04) and smaller for Greece (-0.007). Key Words: Okun s law, uni roos, Medierranean counries. Inroducion Οne of he larges problems ha mos governmens face is unemploymen. Unemploymen can be regarded as he cause of povery and income dispersion. Many scieniss have worked on issues such as unemploymen which is characerized as an imporan power for governmens and also for inernaional economic policies. The main causes of unemploymen and how we can examine i have been explained during he las cenury as a linkage from many facors. Such a cause is ruled from wo imporan laws. The firs one is he demand law for inernal facors, which indicae ha he number of employers changes as long as he labour produciviy, wages demand and price produc changes as well. The second one is he supply law. Employmen level is being suppored on facors such as he saus of an economy and economic cycles, echnological and educaional refinemen and inension, produciviy and profis. The supply surplus in erms of demand is measured as he unemploymen in percenage unis which are available in sociey and is known as ransiional unemploymen. Unemploymen is creaed by defici capial, echnology developmen and from endencies of fall (Kooros 006). The relaionship beween unemploymen rae and he rise of real producion is well known from economiss. Okun (96) using daa from American economy showed ha for every per uni decrease of GNP, he unemploymen rae is increasing more han he naural percenage. Okun pursued o use he relaionship beween he gap of real GNP and he gap of unemploymen rae o predic he poenial GDP given he former relaionship beween unemploymen and GDP. e noed ha changes in unemploymen rae canno be regarded as he referencing poin of he change of real producion which is he resul of he variaed unemploymen. In oher words, here are inermediary facors which connec he unemploymen rae and real producion (Kwami 005). Okun s law was consisen wih he relaionship beween unemploymen rae and real producion for many decades. Even if he negaive relaionship beween he gap of unemploymen rae and he increase of real producion has been quie sable, he absolue value of Okun s coefficien seems o vary in differen ime periods and from counry o counry (Alig e. al 00). A simple specificaion of Okun s law can be he following: (Y Y*) = α + β (UN UN*) + ε () where Y is he naural log of real oupu UN is he unemploymen rae

2 Y* is he poenial oupu UN* is naural rae of unemploymen respecively Prachowny (993) ook a logarihmic linear relaionship from a Cobb-Douglas producion funcion and shown ha Okun s coefficien (β) should be approximaely -0.6 per cen. Of course, he model consised of facors such as produciviy, labour supply and also weekly hour wages. Prachowny s resuls were criicized laer due o shorcomings in he procedure of he daa modeling. Using a curren model, Aoki and Yoshikawa (003) exhibied a relaion beween unemploymen raes and GDP similar o ha of he Okun s law in is business flucuaions. Their simulaion resuls revealed ha Okun s coefficien increases as he average GDP increases. Geidenhuys and Marinkov (007) ried o give answer o he quesion if unemploymen responds o changes in oupu in Souh Africa. For his reason, hey esimaed he relaionship beween economic aciviy and unemploymen rae. The resuls indicaed he presence of an Okun s law relaionship in Souh Africa over he period wih more evidence in favour of asymmeries during recessions. Noor e al (007) examined wheher here exis an Okun ype relaionship beween oupu and unemploymen in he Malaysian economy. The empirical resuls shown ha here was a negaive relaionship beween oupu and unemploymen. Villaverde and Maza (007) analysed Okun s Law for Spain and is seveneen regions over he period Using wo differen derending echniques, he resuls showed an inverse relaionship beween unemploymen and oupu for mos of he Spanish regions and for he whole counry. owever, he values of Okun s coefficiens for hese regions are differen and lower han hose iniially esimaed by Okun and ohers. Perman and Tavera (007) esed for he presence of convergence of he Okun s Law coefficien (OLC) among several alernaive groups of European economies. They used a esing procedure suggesed by Evans in order o invesigae he convergence or non convergence of he OLC in several groups of European counries by examining how he cross counry variance of he OLC evolves over ime in hese groups. A hypohesis of medium erm convergence of he OLC is rejeced for mos of he European counry groups examined. o-chuan uang and Shu-Chin Lin (008), moivaed by a simple heoreical model, proposed he Bayesian approach for esimaing Okun s coefficiens using U.S. quarerly daa from 948: Q o 006: Q. The resuls showed ha here is overwhelming evidence in favor of smooh ime varying Okun s law which is posiively relaed o produciviy rend. Also heir resuls indicaed ha he commonly used Okun s law coefficien can lead o inappropriae resuls. Tururean (008) based on he inflaion rae and unemploymen rae regisered in Romania for he period , examined how o show Okun s Law. Resuls consised of wo disinc models explaining he dependency beween he GDP s growh rae and unemploymen rae s growh and vice versa. This shows ha in he case of Romania here was no wo way relaionship using he same model, he direc and muual dependencies beween growh of unemploymen rae and he growh rae of GDP s as shown in he original formulaion of Okun s Law. Basically, Okun s law consiss of he divergence of real producion and unemploymen rae from long run levels or from employmen levels. Therefore, an imporan sep on Okun s coefficien esimaion is he deerminaion of physical producion and physical unemploymen rae. Unforunaely, hese values are no observable and should be esimaed. Generally, here is no oher way ha his esimaion can be done wih accuracy. For he esimaion of hese values, we use he odrick Presco (997) echnique. This echnique is being used in macroeconomic heory, paricularly in economic cycles heory, in order o find ou ficiious daa and can reduce he high from low frequencies from ime series. The aim of his paper is o esimae Okun s coefficien for four member counries of European Union and o examine he differences ha exis in every counry, hose ha are creaed due o he correspondence of he gap of real producion on he changes of he gap of real unemploymen. The remainder of he paper proceeds as follows. Secion is referred o he role of unemploymen on producion increase of every counry. On secion he daa used in he empirical analysis are described as well as he specificaion of he model. Secion 3 employs wih uni roo ess and examines he saionariy of he daa used. The resuls of his research are presened on secion 4 while secion 5 provides he conclusions of his paper.

3 . Daa and model specificaion As suggesed by Okun (970), here are wo classes of Okun s law specificaions: The gap model and he firs-difference model. According o he gap model, he relaionship beween log of real GDP gap and he unemploymen gap for he four member counries of European Union is he following funcion used: k LGDPGAP = α + βungap + γ LGDPGAP ε () where: j= LGDPGAP is he log of real GDP gap series UNGAP is unemploymen gap series α is he inercep β is he Okun s coefficien o be esimaed. γ is he coefficien o be esimaed. ε is he disurbance erm. j j + This sudy uses daa on he unemploymen rae and real GDP for four Medierranean counries in order o esimae Okun s coefficien. The daa derives from European Economy daa. All series are annual, covering fory wo years (96 00). In his firs research, Okun used daa from Gross Naional Produc. Laer, many academics have esimaed Okun s coefficien using Gross Domesic Produc (arris and Silversone 00) and producion as well (Prachowny 993, and Freeman 000). This paper uses odrick Presco filer (P, wih λ = 00) o decompose he wo ime series wih rend and cyclical componens. The aim of using his filer is o be able o observe he sensiiviy of esimaed Okun s coefficien. An advanage for using he odrick Presco filer is ha ime series which comes ou is saic when we remove he rend (Cogley and Nason 995). The reverse relaionship of he logarihm beween he gap of real GDP and he gap of unemploymen is obvious from he daa ha derives from he four counries ha we examine. The model hypoheses () ake ino accoun ha variables are saionary and he nex sep is o proceed wih he uni roo es using augmened Dickey Fuller es (979) and Kwiakowski e al es (99). 3. Uni roo es Many macroeconomic ime series conain uni roos dominaed by sochasic rends according o Nelson and Plosser (98). Uni roo ess are imporan in examining he saionariy of a ime series, because a non-saionary regressor invalidaes many sandard empirical resuls. The exisence of sochasic rend is deermined by esing he presence of uni roos in ime series daa. In his sudy, uni roo es is being esed using augmened Dickey Fuller es (979) and Kwiakowski e al es (99). 3. Augmened Dickey Fuller es (ADF es) The Augmened Dickey Fuller es (979) is referred o he saisic crierion of δ coefficien on he following regression: k X = δ 0 + δ X - + α i Χ i + u () i= The ADF regression ess for he exisence of uni roo on Χ, namely on logarihm of he gap of real GDP and he gap of unemploymen. The variable Χ -i expresses he firs differences wih k ime lags and final u is he variable ha adjuss he errors of auocorrelaion. The coefficiens δ 0, δ, and α i are being esimaed. The null and he alernaive hypohesis for he exisence of uni roo in variable X is: Η ο : δ = 0 Η ε : δ < 0 This paper follows he suggesion of Engle and Yoo (987) using he Akaike informaion crierion (AIC) (974), o deermine he opimal specificaion of Equaion (). The appropriae order of he model is deermined by compuing Equaion () over a seleced grid of values of he number of k lags and finding ha value of k a which he AIC aains is minimum. The disribuion of he ADF saisic is non- sandard and he criical values abulaed by Mackinnon (99) are used. 3

4 3. Kwiakowski, Phillips, Schmid, and Shin s es (KPSS es) As long as he null hypohesis, in he augmened Dickey Fuller es, is ha ime series consiss of uni roo, he above hypohesis is acceped unless here is dynamic evidence agains i. owever, his approach can have a lower impac agains he saionary uni roo procedure. In conras, Kwiakowski e al (99) presened a es where he null hypohesis is referred o a saionary ime series. KPSS es implemens he augmened Dickey Fuller es considering ha he power for boh ess can be deermined from he comparison of he significance of saisical crieria on boh ess. A saionary ime series has saisical significan crieria for ADF es and non saisical significan crieria on KPSS es (Noe) 4. Empirical Resuls Table presens he resuls of ADF saionariy ess and KPSS ess which were applied on he gap of unemploymen rae and on he logarihm of real GDP for four Medierranean counries on EU in heir levels. Inser Table here: ADF es show ha all variables are saionary on heir levels for he four European counries. Also, KPSS es rejecs he null hypohesis on he levels of ime series for he examined counries. Therefore, he corresponding variables on boh ess (ADF, KPSS) can be characerized as inegraed order null I(0). Table presens he resuls of equaion () for every examined counry. As i was menioned on secion, he gap variables ha are used on equaion (), are saic so here is no need for diversificaion on he daa. Saring wih a maximum of five lags (k=5) of he logarihm of he gap for real GDP which represens he resricions as far as he size of he sample is concerned, we adop a coninuing procedure in order o define he mos suiable srucure for he model s lags. The acceped hypohesis is exacly above he one which produced an imporan resul. The well- ordered hypoheses are as follows: 0 : γ 5 = 0 0 : γ 5 =γ 4 = : γ 5 = γ 4 = γ 3 = : γ 5 = γ 4 = γ 3 = γ = : γ 5 = γ 4 = γ 3 = γ = γ = Inser Table here: 0 The esimaed coefficiens on able are sable enough and saisical significan on 5% level according o odrick and Presco mehod wih an excepion on daa for Greece where coefficien is no saisical significan and has one ime lag. I is worh menioning ha some relaionships migh appear on lags if he direcion is no clear enough. Moosa (997) on he long- run regression of his model, added one period lag on he unemploymen rae in order o inroduce a dynamic on his model. The esimaed Okun s coefficiens are jus an aspec of he variance of unemploymen cos for he four examined counries. The resuls, using odrick and Presco s filer and he mehod of rend removing, sugges ha he cos in he increase per uni on unemploymen rae from he decrease of real GDP is higher in Ialy and lower in Greece. Diagnosic ess for residuals consis of LM es for a possible exisence of auocorrelaion and heeroscedasiciy, he Jarque Bera es for normaliy and Ramsey RESET es for incorrec specificaion of he model wih is funcional form. For he verificaion of forecasing abiliy of he model, he firs and second Chow es were adoped while for he exracion of predicions ou of he sample (Ex ane), he Theil s saisic was used. The main goal of his sudy is no o explain he reason why he cos of unemploymen is higher in Ialy han in oher examined counries. I is obvious ha esimaed Okun s coefficiens are higher in he mos indusrialized counries wih quie larger populaion and producion. 5. Conclusions On his sudy we have esimaed Okun s coefficiens for four member counries of EU using real GDP and unemploymen rae. The purpose of his sudy is o examine he variance on Okun s coefficien for 4

5 he examined counries. Evaluaing he resuls in 5% level of significance, we obain coefficiens sabiliy and saisical resuls for all counries excep Greece. The coefficiens esimaion is for Ialy, for Spain, for Porugal and for Greece and for he EU -5 is -0.. Generally, we can conclude ha we don rejec he esimaions based on resuls of able according o saisical and diagnosic ess. Furhermore, we claim ha he model can predic wihin he sample period saisfacory (Ex Pos). To sum up, we can say ha unemploymen cos from he viewpoin of he loss of real GDP is larger in Ialy, which is regarded as an indusrial counry, and lower in Greece where here is no heavy indusry. References Akaike,. (974). A New Look a he Saisical Model Idenificaion, IEEE Transacion on Auomaic Conrol, AC-9, Aoki & Yoshikawa (003). A new model of labor dynamic: Ulramerics, Okun s law and ransien dynamics, Working Paper. Alig, D., Fizgerald, T., & Ruper P, (00). Okun s law revisied: Should we worry abou low unemploymen? Public Adminisraion and Public Policy, 97, Cogley, T & Nason, J. (995). Effecs of he odrick - Presco filer on rend and difference saionary ime series: Implicaions for business cycle research, Journal of Economics Dynamics and Conrol, 9, Dickey D.A & Fuller W.A, (979). Disribuions of he Esimaors for Auore-gressive Time Series wih a Uni Roo, Journal of American Saisical Associaion, 74, Dickey, D. & Fuller W. (98). Likelihood raio ess for auoregressive ime series wih a uni roo. Economerica, 49, Engle, R.F. & Yoo, B.S. (987). Forecasing and Tesing in Coinegraed Sysems, Journal of Economeris, 35, Freeman, D. (000). A regional es of Okun s law, Inernaional Advances in Economic Research, 6, Geidenhuys, J. & Marinkov, M (007). Robus esimaes of Okun s coefficien for Souh Africa, Working Paper. arris, R., & Silversone, B. (00). Tesing for asymmery in Okun s law: A cross counry comparison, Economic Bullein, 5, 3. uang o-chuan & Lin Shu-Chin (008). Smooh-ime-varying Okun s coefficiens, Economic Modelling, 5, odrick, R., & E. P. Presco (997). Pos war Business Cycles: An Empirical Invesigaion, Journal of Money, Credi, and Banking, 9, 6. Kooros, S., (006). In Search of a General Unemploymen Model, Inernaional Research Journal of Finance and Economics, 4, Kwami,.A., (005). A Cross Province Comparison of Okun s Coefficien for Canada, Applied Economics, 37, Kwiakowski, D., Phillips, P.C., Schmid, P. & Shin, Y. (99). Tesing he Null ypohesis of Saionariy Agains he Alernaive of a Uni Roo. Journal of Economerics, 54, Mackinnon, J. (99). Criical Values for Coinegraion Tess in Long-run Economic Relaionship in Readings in Coinegraion (eds) Engle and Granger, Oxford Universiy Press, New York, Moosa, I. (997). A cross counry comparison of Okun s coefficien, Journal of Comparaive Economics, 4, Nelson, C.R. & Plosser, C.I. (98). Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implicaions, Journal of Moneary Economics, 0, Noor Zaleha Mohd, Nor Norashidah Mohamad & Judhiana Abdul Chani (007). The relaionship beween oupu and unemploymen in Malaysia: Does Okun s law exis? Inernaional Journal of Economics and Managemen, 3, Okun, Α. (970). The Poliical Economy of Prosperiy. Noron: New York. 5

6 Perman, R. & Tavera, Ch (007). Tesing for convergence of he Okun s law coefficien in Europe, Empirica,, 34, Prachowny, M. (993). Okun s Law: Theoreical Foundaions and Revised Esimaes. The Review of Economics and Saisics, 75, Tururean, C (008). Okun s law for Romania during , MPRA Paper No Villaverde, J & Maza, A (007). Okun s law in he Spanish regions, Economic Bullein, 8, -. Noes According o Kwiakowski e al (99), he es of ΚPSS assumes ha a ime series can be composed ino hree componens, a deerminisic ime rend, a random walk and a saionary error: y = δ + r + ε where r is a random walk r = r - + u.. The u is iid (0, σ ). The saionary hypohesis implies ha σ u =0. Under he null, y, is saionary around a consan (δ=0) or rend-saionary (δ 0). In pracice, one simply runs a regression of y over a consan ( in he case of level-saionariy) ore a consan plus a ime rend (in he case of rend-saionary). Using he residuals, e i, from his regression, one compues he LM saisic where S ε is he esimae of variance of ε. LM = T S = e i i= T = u S S / ε, =,, T The disribuion of LM is non-sandard: he es is an upper ail es and limiing values are provided by Kwiakowski e al (99), via Mone Carlo simulaion. To allow weaker assumpions abou he behaviour of ε, one can rely, following Phillips (987) and Phillips and Perron (988) on he Newey and Wes (987) esimae of he long-run variance of ε which is defined as: S ( l) = T T l T ei + T w( s, l) ei = s= = s+ where w(s,l) = - s / (l+). In his case he es becomes ν = T T = which is he one considered here. Obviously he value of he es will depend upon he choice of he lag runcaion parameer, l. ere we use he sample auocorrelaion funcion of e o deermine he maximum value of he lag lengh l. Table : Tess of uni roos hypohesis GREECE S / S ( l) ADF LAGS KPSS BANDWIDT LGDPGAPGR ** *** LGDPGAPGR -6.66*** *** 4 UNGAPGR *** 0.044*** 3 UNGAPGR -4.70*** 0.057*** 3 SPAIN LGDPGAPS ** 0.037*** 3 LGDPGAPS *** *** e i k 6

7 UNGAPS *** 0.04*** UNGAPS -4.54*** 0.046*** ITALY LGDPGAPS *** 0.074*** LGDPGAPS -5.46*** *** 6 UNGAPS -4.85*** 0.034*** 3 UNGAPS *** 0 0.6*** 9 PORTUGAL LGDPGAPS -5.08*** 0.040*** LGDPGAPS -5.83*** 0.36*** 8 UNGAPS -4.59*** 0.043*** UNGAPS *** *** 3 EU-5 LGDPGAPEU ** 0.063*** 4 LGDPGAPEU -4.63*** *** UNGAPEU *** 0.039*** 3 UNGAPEU *** 0.045*** Noes: The -saisic for esing he significance of δ when a ime rend is no included in equaion..the calculaed saisics are hose repored in Dickey-Fuller (98). The criical values a %, 5% and 0% are 3.60, -.90 and.60 for τ µ The KPSS saisics for esing he null hypohesis ha he series are I(0) when he residuals are compued from a regression equaion wih only an inercep respecively. The criical values a %, 5% and 0% are 0.739, and (Kwiakowski e al, 99, able ). ***, **, * indicae significance a he, 5 and 0 percenage levels Table. Esimaed equaion () Consan GREECE ITALY SPAIN PORTUGAL EU-5 [0.9066] -6.3E-05 [0.9899] UNG UNG(-) [0.393] LG(-) [0.0003] [0.06] [0.0003] LG(-) [0.08] [0.886] [0.0000] [0.0000] [0.890] [0.045] [0.000] [0.0384] [0.807] -0.0 [0.000] [0.0000] R () DW (3) Diagnosics Tess Serial Correlaion LM.0 Tes (4) [0.7] [0.86] 0.34 [0.569] 0.89 [0.345].58 [0.08] 7

8 Normaliy Tes (5) [0.] [0.000] [0.5] [0.0] [0.69] Whie 0.96 eeroscedasiciy (6) [0.9].85 [0.065] [0.57].68 [0.069].69 [0.686] ARC LM Tes (7) [0.79] [0.776] [0.675] [0.606] [0.46] Ramsey RESET Tes (8) [0.43] [0.3] [0.38] [0.533] [0.45] Chow Breakpoin 0.03 Tes (9) [0.99] [0.993] 0.98 [0.896] 0.69 [0.957] [0.60] Chow Forecas Tes (0) [0.990] [0.993] [0.963] [0.953] [0.737] Forecasing Theil () Bias Variance Covariance RMSE () MAE (3) MAPE (4) Noes:. Numbers in brackes indicae significan levels.. R = Deerminaion coefficien 3. D-W Durbin Wason saisic for auocorrelaion 4. Breusch Godfrey (Lagrange-Muliplier) es for up o firs order of he residuals. 5. Jarque-Bera es for normaliy of he residuals 6. Whie es for heeroscedasiciy of he residuals 7. ARC Auoregressive condiional heeroscedasiciy saisic of order one. 8. Ramsey rese es of funcional from based on he inclusion of wo fied erms. 9. Chow breakpoin es for break in Chow forecas es from Theil inequaliy coefficien decomposiion ino bias proporion, variance proporion and covariance proporion.. Roo mean squared error. 3. Mean absolue error 4. Mean absolue percen error. 8

Department of Economics East Carolina University Greenville, NC Phone: Fax:

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