6 th Annual Conference of the Hellenic Finance and Accounting Association

Transcription

1 6 h Annual Conference of he Hellenic Finance and Accouning Associaion Convenional Nonlinear Relaionships beween GDP, Inflaion and Sock Marke Reurns. An invesigaion for he Greek Econom. B Dikaios Tserkezos Deparmen of Economics, Universi of Cree. And Eleni Thanou Graduae Program on Banking Hellenic Open Universi Absrac One of he mos enduring debaes in economics is wheher financial developmen causes in a linear or nonlinear manner, economic growh or wheher i is a consequence of increased economic acivi. Lile research ino his quesion has been done for he case of Greece especiall in a nonlinear framework. This paper fills his gap b using simple nonlineari ess o provide evidence of a posiive and significan causal relaionship going from sock marke developmen o economic growh in Greece during he las ears. Kewords Economic growh, capial markes, non-linear causali ess. JEL classificaion G4 Conac deails Universi of Cree, Gallos, GR-74, Rehmno, GREECE. Phone Fa Conac deails Phone , FAX 945 ehanou@oene.gr

2 . Inroducion The invesigaion of he effecs of movemens in he general price level of a sock marke on he economic developmen of a counr as well as he role of inflaionar pressures on GDP growh are issues ha have preoccupied and coninue o be of ineres o researchers of modern applied economics and polic makers alike. In his paper we aemp an invesigaion of non-linear relaionships beween he changes of he real Gross Domesic Produc of he Greek econom (GDP) on he one hand and he reurns of he Greek sock marke and he rae of inflaion on he oher. Using quarerl daa and simple saisical ess of lineari/ non-lineari, we are able o saisicall verif he eisence of non-linear effecs of sock marke reurns and inflaion on he deerminaion of he real GDP of he Greek econom. Ne, we aemp o esablish he direcion of causali beween he variables under eaminaion. In order o invesigae he eisence and direcion of causali we did no use he pical mehods which are based on he use of models wih differen ime lags o pinpoin he presence and direcion of causali. As discussed in secion below, he pical causali ess disribue he effecs among he economic variables involved and esablish simplified causal relaionships, ofen aribuing causali in he presence of co-deerminaion. In he mehodological secion (secion ) of his paper, we demonsrae, using simulaed daa, ha in he presence of nonlineari he pical causali invesigaion models ha use differen ime lags, ofen disribue he effecs among he variables and idenif a bes simplified causali which is in fac due o he co-deerminaion among he variables. The paper proceeds as follows Secion provides an overview of he mehodolog used, uilizing simulaed daa in order o he choice of our model. Secion 3 analses he available daa, while in secion 4 we presen he resuls of he empirical analsis. Finall, Secion 5 conains he concluding remarks and implicaions for furher research.

3 . Mehodolog The main goal of his sud is o eamine he eisence of linear or non-linear effecs from he sock marke (sa ) and he rae of inflaion (sa ) on he deerminaion of he Gross Domesic Produc (sa ). = f (,, parameer ) () The basic es is o check wheher he effecs of he wo dependen variables (, ) on he dependen variable () are linear or non-linear, ha is we will eamine he form of he following relaionships και () One basic assumpion we make in our analsis is ha here are no feed-back effecs from he dependen variable (GDP) o he independen variables and. This is no an unrealisic assumpion, given ha our daa are quarerl. The use of quarerl daa is dicaed b he fac ha real GDP figures are no available for shorer periods 3. Given his resricion, i is logical o assume ha an feedback is ehaused wihin he quarer so ha he bes approach is o model he relaionships among he variables in a saic environmen. However, his is no he onl raionale for our approach, as shown in he following secions.. Causali es performance in he presence of non-lineari. The main reason, in our opinion, ha jusifies he use of a saic model o es for lineari or non-lineari, is ha he use of disribued lag models or crieria based on disribued lag specificaions ma ofen lead o non reliable conclusions on he was ha he economic variables under invesigaion are relaed. In he following secion, wih he use of simulaed, consruced daa, we es alernaive mehodologies used o esablish causali and we are able o demonsrae ha he use of disribued lag specificaions ma disribue he diachronic effecs from he 3 Sock marke reurns eis on a dail basis while inflaion is available monhl 3

4 dependen variables in an arbirar wa, even hough such effecs were no presen in he original series... The Mone Carlo Eperimens. Our simulaion eperimen is based on he following nonlinear in he variables and parameers rue specificaion 3.34 (3).45 NID(.5) Four eogenous variables were generaed using he following processes w i,,3 (4) i ( ( i) ) w NID(.5) wih.. 5 and 3.95 (5). The values (5) of he parameers of he specificaion (4) were chosen o give differen auoregressive characerisics on he daa generaing processes of he eogenous variables. Eperimens wih independen variables wih ime rends were also underaken. In his case we assumed ha he independen variables were generaed as follows ep( TR ) (6) j j j NID( Uniform(.5,.5)), Uniform(.,.67) j and TR,,... (Time Trend). j Using he simulaed daa generaed wih he help of relaionships (3) o (6), we hen appl he following ess A. Non-lineari ess The non-lineari ess uilized in his sud are based on he classic Wald es. We es he hpohesis ha = f (,, parameer ) 4

5 5 or more specificall, (7) Agains he hpoheses 8,,, H H H H H H The esing of above hpoheses will be conduced using Wald s crierion, he applicaion of which requires he esimaion of non-linear model (7). The esimaion of he parameers of model (7) is based on he linearizaion (Talor epansion) shown below Walds es is applied on he model Wald s es consiss of he compuaion of he saisic for each hpohesis of (8) as follows s H s H If i is proven ha and are saisicall differen from, hen we prove he eisence of non lineari such as (7). B. The Alernaive Procedures Tesing Linear Granger Causali. In order o compare he performance of Wald s non-lineari es wih he alernaive mehodolog used for esing linear causali, we applied on our simulaed daa Hsiao's (98) linear causali es. The es is based on a bivariae VAR represenaion for wo saionar series and. Hsio's sequenial procedure for linear causali is based on he bivariae VAR represenaion q j j j n i i i, (9)

6 n q i i j j, i j () and where and does no cause are saionar variables and n and q are he lag lenghs of respecivel. The null hpohesis in he Granger causali es is ha hpohesis is which is represened b H, i q and he alernaive H for a leas one j in Equaion (9). The es saisic has a sandard F disribuion wih (n, T-n-q-) degrees of freedom, where T is he number of observaions. Akaike Informaion Crierion is used o find he opimal lag lenghs for boh and. Hsiao (98) has suggesed a sequenial procedure for causali esing ha combines Akaike's final predicive error crierion (FPE) and he definiion of Granger causali. To es for causali from seps o,he procedure consiss of he following. Trea as a one-dimensional process as represened b Eq. () wih j = j, and compue is FPE wih n varing from o L, which is chosen arbiraril. Choose he n ha gives he smalles FPE, denoed FPE_( n, ).. Trea as a conrolled variable, wih n as chosen in sep and as a manipulaed variable as in Eq. (). Compue he FPE's of Eq. () b varing he order of lags of FPE_( n, q ). from o L and deermine q, which gives rue minimum FPE, denoed 3. Compare FPE_( n, ).) wih FPE_( n, q ). If he former is greaer han he laer, hen i can be concluded ha causes..3 The Mone Carlo Simulaion resuls. Afer a large number of daa series were generaed using he simulaion model (3)-(6), we used hem o calculae he non-lineari and causali ess, aiming o validae e pos he accurac of hese ess. The resuls of appling he nonlineari and linear causali ess on our simulaed daa are shown in graphs -4 6

7 below. 4 On he horizonal ais of each graph we displa he number of observaions of he independen variable, while on he verical we represen he percenage of successful idenificaion of causali from variable rejecion of he hpohesis of feedback effecs ( ) op line represens analogous resuls using Wald s crierion. o variable ( ) and beween he variables. The 9 RES() RES(3) RES(4) Graph. Percenage of successful idenificaion of causali from and rejecion of he feedback from for RES(8) RES(9) RES() Graph. Percenage of successful idenificaion of causali from and rejecion of he feedback from for. 5 4 Analical numerical resuls of our eperimens can be made available upon reques o ineresed researchers. 7

8 8 7 RES() RES() RES(3) Graph 3. Percenage of successful idenificaion of causali from and rejecion of he feedback from for RES(4) RES(5) RES(6) Graph 4. Percenage of successful idenificaion of causali from and rejecion of he feedback from in he presence of ime rends in (eq 6) The resuls of our eperimens are quie revealing In graphs -3, he Wald es (op line) performs beer han he linear causali es. In he cases where a saic nonlinear relaionship eiss b design, beween and, he applicaion of Hsiao s linear causali es disribues he effec of diachronicall. In he opposie case, 8

9 he use of classic non-lineari successfull (99%) idenifies a more represenaive rendering of heir rue relaionship. Anoher ineresing observaion comes from he analsis of he auocorrelaion characerisics of independen variable. As he auocorrelaion coefficien approaches one, hen he percenage of he successful idenificaion of he relaionship beween he wo variables decreases. Anoher observaion is ha as he number of observaions increases, he probabili of successful idenificaion of he rue relaionship beween he variables increases, ecep in he case of srong ime rends in he eogenous variable. i 3. The daa used in he sud. The empirical analsis is carried ou using quarerl daa for he period 984Q Q4 for Greece. The oupu variable is he real Gross Domesic Produc (GDP), he price level is he consumer price inde (CPI) and he sock marke variable is he value of he Ahens Sock Echange General Inde (STOCK). Domesic real sock reurns (DLRSTOCK) is he difference beween he coninuousl compounded reurn of he ASE General Inde and he Greek inflaion rae, which is calculaed using he consumer price inde. All daa are aken from he Bullein of Conjecural Indicaors of he Bank of Greece, are no seasonall adjused and can be found in he appendi. For he applicaion of he saisical ess for non-lineari in he relaionships among he variables under invesigaion, he available daa were firs epressed in logarihms (LGDP, LRSTOCK, LCPI) and hen heir firs differences were aken, due o presence of saionari in he daa. 4. The resuls Using he above described daa series, we firs esed wheher he relaionship among he variables is non-linear, esing he following hpoheses (7) 9

10 Η Η Η = = = = ha Appling Wald s crierion o he esimaed parameers of (7), we concluded s =,86 = 4,5,6 s =. = As he values for he esimaed parameers γ and γ are much higher han he value of he -disribuion,,96 for a large sample wo-ailed es a he 5 percen significance level, we rejec he null hpohesis of a linear relaion beween hese hree variables in favor of a nonlinear specificaion. The presence of non-lineari in he effecs from he wo eogenous variables, χ and χ, ha is he percenage changes in he value of ASE General Inde and he changes in he Consumer Price Inde (rae of inflaion) on he evoluion of he real GDP of he Greek Econom, is of significan imporance. Non-lineari implies ha he effecs are ver differen in differen ranges of he values of he variables. In graphs Graphs 5 and 6 below we presen hese effecs based on he esimaed relaionships d d and d ( ) ln( ) d

11 d d d ( ) = ln( ) d Graph 5 The effec of changes in he value of he sock marke inde on he evoluion of he Gross Domesic Produc Graph 6 The effec of changes in he rae of inflaion on he evoluion of he Gross Domesic Produc. As can be seen in graph 5, he relaionship beween changes in he sock marke value and he GDP is generall posiive, as epeced from heor and

12 confirmed b a number of oher sudies, bu he effec of he flucuaions in he sock marke on real GDP is significanl differen when he changes in he sock inde are in he negaive range, compared o he effecs in he case of posiive flucuaions. The shape of he curve shows ha when he sock marke is moving in negaive grounds, an change in he inde has a sronger effec on he real GDP compared o a bullish marke, where a % flucuaion in he value of he inde has a weaker effec on he real econom. Moreover, he effecs become asmpoicall zero as we approach posiive values of real GDP growh. Similarl, in graph 6 we observe ha he overall effec of inflaion on real GDP is negaive, as epeced from heor. Again, small changes in he inflaion rae (around he verical line) have a sronger negaive impac on changes in real GDP whereas he effecs are weaker, he higher he inflaion rae. Here we use he acual inflaion of he same period and we do no differeniae beween anicipaed and unanicipaed inflaion as do oher sudies focused on he subjec. Neverheless, he fac ha non-lineari is presen implies ha he effecs are differen for differen ranges of values of he variables under sud. 5. Conclusions This sud conribues o he eensive lieraure ha invesigaes he role of capial markes flucuaions and he rae of inflaion on he real GDP. Using simple non-lineari ess we were able o demonsrae ha for he Greek econom and he period under invesigaion, changes in he value of he sock marke and in he rae of inflaion affec he evoluion of real GDP in a non-linear wa. While he sock marke has a posiive effec on real GDP growh, his effec weakens he higher he sock marke s rae of change. Similarl for inflaion, here is a negaive relaionship ha becomes weaker he higher he rae of inflaion. The case of Greece, over he period 984, serves as an eample in our empirical invesigaion. Greece is a counr wih less maure financial markes compared o oher advanced economies. Over he las wo decades, is financial ssem was liberalized a an acceleraing pace and epanded considerabl, while he fairl remarkable growh raes achieved b he Greek econom afer he earl 99s

13 enabled he counr o ener he Euro zone in. We hink ha he conclusions drawn could be useful for he analsis of oher medium-sized economies, such as he Cenral and Easern European counries, which have recenl joined he European Union. 3

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