volatiltiy transmission and fnancial crisis

8/8/2019 Volatiltiy Transmission and Fnancial Crisis

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376 J O U R N A L O F E C O N O M I C S A N D F I N A N C E 9 Volume 30 9 Nu m b er 3 9 Fall 2006V O L A T I L I T Y T R A N S M I SS I O N A N D F I N A N C I A L

C R I S E SB y G u g l i e l m o M a r i a C a p o r a le , N i k i t a s P i tt is , a n d N i c o l a S p a g n o l o ~A b s t r a c t

I n t h is p a p e r w e e x a m i n e t h e i n te r n a t io n a l t r a n s m i s s io n o f t he 1 9 9 7 S o u t h E a s t A s i a f i n a n c i a lc r is is . W e e st i m a t e a b i v a r ia t e G A R C H - B E K K m o d e l a n d c a r r y o u t L R t e s t s f o r c a u s a l i t y- i n -v a r i a n c e w i t h b o o t s t r a p p e d c r i t ic a l v al ue s . T h r e e p a i r w i s e m o d e l s a r e e s t i m a t e d f o r U S ,E u r o p e a n , J a p a n e s e a n d S o u t h E a s t A s i a n d a i l y s t o c k m a r k e t r e t u r n s . V o l a ti li ty s p i l l o v e r s a r efo u n d i n a l l cases . Th e d yn a mics o f t h e co n d i t i o n a l v o la t i li t ie s d if f er , b u t ca u sa l i t y l i n k s in t h ev a r i a n c e a r e f o u n d t o b e s t ro n g a n d b i d i r e c ti o n a l i n n o r m a l p e r io d s , a n d u n i d i r e c ti o n a l ( f r o m t h em a r k e t s i n tu r m o i l t o th e o t h e r s ) f o l l o w i n g t h e o n s e t o f th e c r i si s , c o n s i s te n t l y w i t h c r i si s -co n t in g en t mo d e l s . ( J E L C 3 2 , G 1 5 )

In t roduc t i onT h e r e l a ti v e i m p o r t a n c e o f m a c r o e c o n o m i c a n d fi n a n c i a l s e c t o r l i n k a g e s i n e x p l a i n i n g

c o n t a g i o n b e t w e e n c o u n t r i e s o r r e g i o n s f o l l o w i n g t h e o n s e t o f a f i n a n c i a l c ri s is i s o f t e n d e b a t e d .A t t h e ti m e o f t h e 1 9 9 7 S o u t h E a s t A s i a c ri s is , b o t h t h e O E C D a n d t h e I M F t r ie d t o q u a n t i f y i tsl i k el y a d v e r s e e f f e c t s o n o u t p u t g r o w t h i n t h e i n d u s tr i al e c o n o m i e s b y f o c u s i n g o n t r a d e l i n k a g e s .F o r i n s ta n c e , t h e O E C D e s t i m a t e d t h a t a s l o w d o w n i n t r a d e w i t h A s i a c o u l d r e s u l t in a fa ll o fn e a r l y 1 p e r c e n t i n t h e le v e l o f G D P o v e r t w o y e a r s in t h e O E C D a r e a a s a w h o l e ( s ee O E C D ,1 9 9 7 ). O t h e r s t u d ie s a r g u e d t h at , b e c a u s e t r a d e i s m a i n l y r eg i o n a l , c o n t a g i o n t e n d s t o b e b e t w e e ne c o n o m i e s w i t h in t h e s a m e r e g i o n ; th i s is t r u e b o t h o f c o u n t r i e s w h i c h a r e c o m p e t i t o r s , h a v i n gs i m i la r e x p o r t s ( s ee G l i c k a n d R o s e , 1 9 9 9 ), a n d o f c o u n t r ie s w h i c h a r e c o m p l e m e n t s , b e i n g a td i ff e re n t s ta g e s o f e c o n o m i c d e v e l o p m e n t ( s ee D i w a n a n d H o e k m a n , 1 9 9 8) . H o w e v e r , w h e t h e rt r a d e l i n k a g e s a r e a c r u c i a l c h a n n e l f o r c o n t a g i o n is an e m p i r i c a l m a t t e r , a n d t h e e v i d e n c e i s n o tu n e q u i v o c a l l y s u p p o r t i v e o f t hi s id e a . T h e O E C D i t se l f a c k n o w l e d g e d t h a t tr a d e f l o w s a r e o n l yo n e o f th e p o s s i b l e t r a n s m i s s i o n m e c h a n i s m s - it is v it al t o t a k e i n t o a c c o u n t s p i l l o v e r s a c r o s sg l o b a l f in a n c i a l m a r k e t s w h e n a n a l y s i n g t h e p o s s i b l e r e p e r c u s s i o n s o f f i n a n c i al t u r b u l e n c e i n o n er e g i o n o n o t h e r r e g i o n s o f th e w o r l d . I n f a c t a s t u d y b y t h e I M F , w h i c h t e s t ed f o r f i n a n c i al m a r k e tc o n t a g i o n w i t h i n S o u t h E a s t A s ia , f o u n d a n in c r e a s e i n th e c o r r e la t i o n s b e t w e e n f i n a n c ia l m a r k e t sd u r i n g a c r i s i s c o m p a r e d t o a t r a n q u i l p e r i o d ( s e e B a i g a n d G o l d f a j n , 1 9 9 8 ) .

A d m i t t e d l y , t h e n a t u r e o f c o n t a g i o n i s d i ff i c u l t to i d e n ti f y . F o r i n s ta n c e , a l t h o u g h t h e r e i se v i d e n c e t h a t a s s e t p r i c e s a r e h i g h l y c o r r e l a t e d a c r o s s S o u t h E a s t A s i a , i t i s n o t c l e a r w h e t h e r t h i sr e f l e c ts s i m i l a r i ti e s i n f u n d a m e n t a l s o r is a c o n s e q u e n c e o f s p i l l o v e r s ( s e e A l b a e t a l, 1 9 9 8 ) .H o w e v e r , t h e r e i s a g r o w i n g c o n s e n s u s t h a t a n a l y s i n g f i n a n c i a l c o n t a g i o n i s e s s e n t i a l t ou n d e r s t a n d i n g f i n a n c ia l c r is e s, e s p e c i a l l y i n v i e w o f th e i n c r e a s i n g d e g r e e o f in t e g r a t io n o fi n t er n a t io n a l f i n an c i a l m a r k e ts . F o r i n s t an c e , M a s s o n ( 1 9 9 9 ) d e v e l o p e d a m o d e l i n w h i c hc o n t a g i o n g e n e r a t e s a c r i s i s t h r o u g h i t s c a p i t a l a c c o u n t e f f e c t s ( e v e n t h o u g h t h e u n d e r l y i n g

The authors are grateful to an anonym ous referee, Graciela Kam insky, M arco Barassi, Andrea Cipollini andparticipants in the 2001 AEA M eetings, New Orleans, January 5-7, 200 1, and in the A ustralasian Meeting of theEconom etric Society, Auckland, New Z ealand, July 6-8, 2001 for useful comm ents and suggestions. Financial assistancefrom Leverhulme grant F/71 l/A, "Volatility of share prices and the macroeconom y: eal effects of financial crises", is alsogratefully acknowledged. Corresponding author: Professor Guglielmo Maria Caporale, Brunel Business S chool, BrunelUniversity, Uxbridge, Middlesex UB8 3PH , UK. Tel.: +44 (0)1895 266713. Fax: +44 (0)1895 26 9770. E-mall: Guglielmo-M aria.Caporale @brunel.ac.uk


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JOURNAL OF ECONOMICS AND FIN ANCE * Volume 30 oNumber 3 9 Fall 2006 377m e c h a n i s m w o r k s t h r o u g h t r a d e c h a n n e l s ) . K a m i n s k y a n d S c h m u k l e r ( 1 9 9 9 ) e m p h a s i s e d t h epos s i b l e " he r d i ng" be ha v i ou r o f inve s t o r s w h o j u s t f o l l ow t h~ m a r ke t be l i e v i ng t ha t a s s e t p r i c e sc on t a i n r e l e va n t i n fo r m a t i on ; a s a r e su l t , t he r e c ou l d be a s t oc k m a r ke t cr i s i s in o ne c o un t r y s i m p l ybe c a us e o f t he c o l la ps e w h i c h ha s oc c u r r e d i n a no t he r c oun t r y . C l e a r ly , a s u r ge i n t he vo l a t i l it y o fs t oc k p r i c e s c a n t he n ha ve a s i gn i f i c a n t i m pa c t on t he r e a l e c onom y t h r ough , e . g . , w e a l t h e f f e c t sa nd t he c os t o f c a p it a l. D i r e c t r e a ll oc a t i on o f re s ou r c e s a nd ha l te d o ve r s e a s a c t iv i t ie s , o r r e s o u r c er e a l l oc a t i on invo l v i ng t he ba nk i ng s e c t o r , c a n a l s o be ve r y i m por t a n t a s a t r a ns m i s s i on m e c ha n i s mfrom the f inanc ia l to the r ea l s ec tor . This was ce r ta in ly the ca se in South Eas t As ia in 1997, w i tht he c r is i s a f fe c t ing ove r s e a s s ubs i d i a ri e s a nd s ub c on t r a c t o rs o f A s ia n c o m p a n i e s , a nd t hus t he l oc a le c o n o m i e s .

E x i s t i ng e m p i r i c a l s t ud i e s a na l y s e p r i m a r i l y dyna m i c l i nka ge s be t w e e n de ve l ope d m a r ke t s ,w i t h on l y s om e o f t he m f oc us i ng on l i nka ge s be t w e e n e m e r g i ng m a r ke t s , o r be t w e e n t he s e a ndo t he r f o r e i gn m a r ke ts . F u r t he r m o r e , m os t e m p i r i c a l s t ud ie s on l y c ons i de r l i nka ge s be t w e e n f i r s tm om e n t s , na m e l y t he y l ook a t c o r r e l a t i ons , i . e . f i r s t - o r de r de pe nde nc e i n a l i ne a r r e g r e s s i onf r a m e w or k ( s e e , e . g . , H i l l i a r d ( 1979 ) , E un a nd S h i m ( 1989 ) a nd K oc h a nd K oc h ( 1991 ) , w ho a l le xa m i ne d t he c on t e m por a n e ous a nd l a gge d c o r r e l a t i on i n da i l y p r i c e c ha ng e s a c r o s s m a j o r s t oc km a r ke t s ). T h e pos s i b i li t y o f h i ghe r - o r de r de pe nde nc e , a r i s ing ou t o f the i n t e r a c ti ons be t w e e n t hes e c ond m om e n t s , ha s ha r d l y be e n i nve s t iga t e d , e ve n t hough t he i m p or t a nc e o f s e c ond c on d i t i ona lm om e n t s i n m ode l l i ng h i gh f r e que nc y f i na nc i a l t i m e s e r i e s ha s be e n r e c ogn i z e d e ve r s i nc e E ng l e( 1982 ) i n t r oduc e d the c la s s o f A R C H m ode l s . I n t e rm s o f e s ti m a t i on t e c hn i que s , t he G A R C Hf r a m e w or k i n va r i ous f o r m s p r e dom i na t e s . A f e w e xc e p t i ons u s e V A R o r c o i n t e g r a t i on a na l y s i s .F o r i n s t a nc e , L i u a nd P a n ( 1997 ) e s t i m a t e d a V A R t o e xa m i ne t he dyna m i c r e l a t i ons h i p s be t w e e nA s i a n - P a c i f i c s t oc k m a r ke t s . S a nde r a nd K l e i m e i e r ( 2003 ) c a r r i e d ou t c o i n t e g r a t i on a nd G r a nge rc a us a l i t y t e s t s t o a na l y s e c on t a g i on be t w e e n s ove r e i gn bond s p r e a ds a s a m e a s u r e o f pe r c e i ve dc oun t r y r is k i n f ou r A s i a n c r i s is e p i s ode s . T h e y c ons i de r e d l i nka ge s w i t h i n t he A s i a n r e g i on , a n da l s o be t w e e n A s i a a nd o t he r e m e r g i ng e c onom i e s , a nd f ound e v i de nc e f o r c ha nge d c a us a l i t ypa t te rns on a r eg ion a l l eve l , and a l so on a g loba l l eve l a s the Russ ian c r i s i s s t a r ted .S t ud i e s f oc us ing on t he de ve l ope d m a r ke t s a re num e r ous . F o r i n s t a nc e , H a m a o e t a l . ( 1990 )e m pl oye d a u t o r e g r e s s i ve c ond i t i ona l l y he t e r o s c e da s t i c m ode l s t o s t udy t he dyna m i c s o f s p i l l ove re f f e c t s i n p r i c e c ha nge s a nd vo l a t i l i t y be t w e e n t he U S a nd J a pa n , a nd f ound t ha t s hoc ks t ha tor ig ina te in the US a re l a rge r and more pe r s i s ten t . L in e t a l . (1994) , us ing a s igna l ex t rac t ionm o d e l w i t h G A R C H p r o c es s es , st u d i ed t h e N e w Y o r k a n d T o k y o s t o c k m a r k e t s a n d f o u n df e e dba c k e f f e c t s be t w e e n t he s e t w o m a r ke t s . S us m e l a nd E ng l e ( 1994 ) a na l y s e d t hei n t e r r e l a t i ons h i p be t w e e n t he N e w Y or k a nd L ondon s t oc k m a r ke t s a nd d i d no t f i nd m uc he v i de nc e o f e i t he r m e a n o r vo l a t i l i t y s p i l l ove r s . T he y a r gue d t ha t e a r l i e r f i nd i ngs t o t he c on t r a r yw e r e due t o t he u s e o f non - r obus t e s t i m a t o r s w i t h t he a s s oc i a t e d s t a nda r d e r r o r s be i ng t oo s m a l l .K a r o l y i ( 1995 ) e xa m i ne d t he dyn a m i c r el a t ions h i p be t w e e n U S a nd C a na d i a n s t oc k m a r ke t r e t u r n sa nd r e t u r n vo l a t i l i t i e s u s i ng a b i va r i a t e ge ne r a l i z e d a u t o r e g r e s s i ve c ond i t i ona l he t e r o s c e da s t i cm ode l . H e f ound tha t the e f f e c ts o f s hoc ks f r om t he S & P 500 i nde x r e tu r n s on t he T S E 300 i nd e xr e t u r n s a nd vo l a t i l i t y a r e s m a l l e r a nd l e s s pe r s i s t e n t t ha n t hos e m e a s u r e d w i t h t r a d i t i ona l ve c t o ra u t o r e g r e s s i ve m ode l s . T he odos s i ou a nd L e e ( 1993 ) s t ud i e d t he r e l a t i ons h i p be t w e e n t he U S , U K ,C a na d i a n , G e r m a n a nd J a pa ne s e s t oc k m a r ke t s u s i ng a m u l t i va r i a t e G A R C H - i n - m e a n m ode l a ndf ound m e a n a nd vo l a t i li t y s p i l love r s be t w e e n s om e o f t hos e m a r ke t s . A m i no r i t y o f s t ud i e s f oc uson vo l a t i li t y s p i l love r s w i t h i n i nd i v idua l de ve l op e d s t oc k m a r ke t s ( s e e , e .g . , R e ye s , 2001 ,c ons i de r i ng t he T okyo s t oc k e xc ha nge ) , o r on l i nka ge s be t w e e n f i na nc i a l m a r ke t s ( c om m od i t y ,f o r e i gn e xc ha ng e , bond a nd s t oc k m a r ke t s ) i n t he s a m e c oun t r y ( se e , e . g . , D a r ba r a nd D e b , 1999 ,a na l y s i ng the U S c a s e ). O nc e a ga i n , t he y a r e ba s e d on s om e t ype o f G A R C H m o de l - b i va r ia t ee x p o n e n t i a l G A R C H ( E G A R C H ) a n d b i v a r i a t e L o g i s t i c E G A R C H ( L E G A R C H ) r e s p e c t i v e l y .

F e w e r pa pe rs ha ve l ooke d a t l i nka ge s be t w e e n e m e r g i ng m a r ke t s . O ne e x a m p l e i s the a l r e a dym e n t i o n e d V A R a n a l y i s b y L i u a n d P a n ( 1 9 9 7 ) e x a m i n i n g i n f o r m a t i o n t r a n s f e r s b e t w e e n J a p a na nd ne i ghb ou r i ng A s i a n - P a c i f i c m a r ke t s . W or t h i n g t on e t a l. ( 2001 ) l oo k a t p r ic e l i nka ge s i n A s i a n


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37 8 JOURNAL OF ECONOMICS AND FINA NCE 9 Volume 30 9 Numb er 3 9 Fall 200 6e q u i t y m a r k e t s u s i n g a m u l t i v a r i a te c o i n t e g r a t i o n p r o c e d u r e . S o l a e t a l. ( 2 0 0 2 ) p r o p o s e a n e wp r o c e d u r e f o r a n a l y z i n g v o l a t i l i t y l i n k s b e t w e e n d i f f e r e n t m a r k e t s b a s e d o n a b i v a r i a t e M a r k o vs w i t c h i n g m o d e l . T h e y f i n d t h a t v o l a t il i ty s p i l l o v e r s b e c o m e u n i d i re c t io n a l f o l l o w i n g t he o n s e t o ft h e t 9 9 7 c r is i s, r u n n i n g f r o m T h a i l a n d ( t h e m a r k e t i n tu r m o i l ) t o S o u t h K o r e a , w h i l s t B r az i l w a sh a rd ly a f fec t ed .S i m i l a r l y , o n l y a f e w p a p e r s h a v e i n v e s t i g a t e d t h e r e l a t i o n s h i p b e t w e e n d e v e l o p e d a n de m e r g i n g m a r k e t s . L i u e t a l. ( 1 9 9 8 ) u s i n g a V A R m e t h o d o l o g y e x a m i n e t h e s t ru c t ur e o fi n t e rn a t i o n a l t r an smi ss io n s i n d a i l y re tu rn s fo r s i x n a t i o n a l s t o ck mark e t s . Th e i r r e su l t s i n d i ca t et h a t t h e U S m a r k e t p l a y s a d o m i n a n t r o l e i n i n f l u e n c i n g t h e P a c i f i c - B a s i n m a r k e t s ; J a p a n a n dS i n g a p o r e t o g e t h e r h a v e a s i g n i f i c a n t p e r s i s t e n t i m p a c t o n t h e o t h e r A s i a n m a r k e t s , w h i l e t h em a r k e t s i n T a i w a n a n d T h a i l a n d a r e n o t e f f i c i e n t i n p r o c e s s i n g i n t e r n a t i o n a l n e w s . F u r t h e r m o r e ,C h e u n g e t a l. (2 0 0 2 ) s t u d y t h e in t e r a c ti o n s b e t w e e n t h e U S , J a p a n a n d f o u r E a s t A s i a n m a r k e t s .T h e y r e p o r t e d t h a t t h e U S m a r k e t l e d t h e A s i a n m a r k e t s b e f o r e a n d a f t e r t h e c r i s i s , b u t w a sG r a n g e r - c a u s e d b y t h e s e m a r k e t s d u r i n g t h e c r i s i s p e r i o d . D u r i n g t h e s a m e p e r i o d , t h e E a s t A s i a nm a r k e t w e r e a f f e c t e d b y t h e J a p a n e s e o n e . W a l t i ( 2 0 0 3 ) a l s o te s t e d f o r t h e e x i s te n c e o f c o n t a g i o nd u r i n g th e r e c e n t A s i a n c r i s e s u si n g th e f r a m e w o r k o f F a v e r o a n d G i a v a z z i ( 2 0 0 2 ) a n d f o u n d t h a tt h e h y p o t h e s is o f n o c o n t a g i o n is w i d e l y r e j e c t e d .

G i v e n t h e f a c t t h a t a l l r e c e n t c u r r e n c y a n d f i n a n c i a l c r i s e s o r i g i n a t e d i n e m e r g i n g m a r k e t s( e .g . , M e x i c o i n 1 9 9 4 , a n d S o u t h E a s t A s i a i n 1 9 9 7) , b e f o r e a f f e c ti n g t h e d e v e l o p e d e c o n o m i e s ,an d i n v a r i ab ly l ed t o su b s t an t i a l l y mo re v o l a t i l e s t o ck p r i ce s , i t i s o f p a r t i cu l a r i n t e re s t t o fo cu s o nv o l a t il i ty tr a n s m i s s i o n a c r o s s e m e r g i n g a n d d e v e l o p e d s t o c k m a r k e t s , a s th e p r e s e n t p a p e r d o e s . I nl in e w i t h th e v a s t m a j o r i t y o f e x is t i n g s tu d i e s , w e t a k e a G A R C H m o d e l i n g a p p r o a c h . S p e c i f ic a l ly ,w e e s t im a t e a b i v a r ia t e G A R C H m o d e l ~, f o r w h i c h a B E K K r e p r e se n t a ti o n i s a d o p t e d ( s e e E n g l ea n d K r o n e r , 1 9 9 5 ) , a n d t h e n t e s t f o r t h e r e l e v a n t z e r o r e s t r i c t i o n s o n t h e c o n d i t i o n a l v a r i a n c ep a r a m e t e r s b y m e a n s o f l i k e li h o o d r a t i o ( L R ) t e s t s , a s in o t h e r s t u d ie s s u c h a s C h e u n g e t al., 2 0 0 2 .H o w e v e r , r a t h e r t h a n r e l y i n g o n a s y m p t o t i c d i s t r i b u t i o n s , w e u s e a p p r o p r i a t e l y b o o t s t r a p p e dc r i ti c a l v a lu e s . T h i s i s b e c a u s e e m p i r i c a l d i s t r ib u t i o n s c a n d i f f e r f r o m t h e a s y m p t o t i c o n e s, a n dt h e r e f o r e f o r t h e p u r p o s e o f s ta t is t ic a l i n f e r e n c e i t i s o f p a r a m o u n t i m p o r t a n c e t o o b t a i n t h e fo r m e r .I n t h i s r e s p e c t , o u r s t u d y i m p r o v e s s i g n i f i c a n t l y o n e a r l i e r o n e s , w h i c h d o n o t a d d r e s s t h e f i n i t es a m p l e is s u e s, a n d h e n c e i t p r o v i d e s m o r e r e l i a b l e e v i d e n c e . W e u s e t h i s f r a m e w o r k t o a n a l y z e t h e1 9 9 7 S o u t h E a s t A s i a c r i s i s , a n d a s k t h e q u e s t i o n w h e t h e r i t s o n s e t a f f e c t e d t h e v o l a t i l i t yt r a n s m i s s i o n m e c h a n i s m a n d c h a n g e d i n t e r n a t i o n a l f i n a n c i a l l i n k a g e s . W e f i n d t h a t , p r i o r t o t h ec r i s i s , t h e r e w e r e b i d i r e c t i o n a l v o l a t i l i t y s p i l l o v e r s b e t w e e n t h e S o u t h E a s t A s i a n , E u r o p e a n ,J a p a n e s e a n d U S s t o c k m a r k e t s . B y c o n t r a s t , i n t h e p o s t - c r i s i s p e r i o d s c a u s a l i t y l i n k s b e c a m eu n i d ir e c ti o n a l, r u n n i n g o n l y f r o m t h e S o u t h E a s t A s i a n m a r k e t s , w h e r e t h e c ri s is o r i g i n a te d , t o t h eo th e rs .T h e l a y o u t o f t h e p a p e r i s as f o l lo w s . T h e n e x t s e c t io n o u t l in e s t h e b i v a r i a t e G A R C H m o d e lu s e d t o s t u d y v o l a t i l i t y s p i l l o v e r s b e t w e e n s t o c k m a r k e t s . S e c t i o n 3 d e s c r i b e s t h e d a t a a n d t h ep ro ced u re u sed t o ca l cu l a t e t h e ap p ro p r i a t e b o o t s t rap ca l i b ra t ed l i k e l i h o o d ra t i o t e s t , an d rep o r t st h e e m p i r ic a l e s t im a t e s . T h e f i n a l s e c t i o n o f f e r s s o m e c o n c l u d i n g r e m a r k s .

1The concept of causality in the second mom ents can be thought of as an extension of the well-established notion ofGranger causalitybetween the first moments, and it could be tested empiricallyby employing he test recentlyproposed byCheung and Ng (1996).


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J O U R N A L O F E C O N O M I C SA N D F I N A N C E 9 V o lu m e 3 0 9 N u m b e r 3 9 Fa l l 2006T h e M o d e l

3 7 9

I n t h is s e c ti o n , w e i n t r o d u c e t h e m u l t i v a r i a t e G A R C H p r o c e s s w e e m p l o y t o e s t im a t e t h ei n te r n a t io n a l t r a n s m i s s i o n o f s t o c k r e tu r n s ' v o l a t il i ty . W e m o d e l t h e j o i n t p r o c e s s e s g o v e r n i n g t h er a t e s o f r e t ur n s o f t w o s t o c k i n d i c e s w i t h t h e f o l l o w i n g b i v a r i a t e G A R C H m o d e l 2 9

r t = a ' + / ~ r t _ 1 + u , ( 1)

w h e r e t h e r e s i d u a l v e c t o r u~ = ( e ~ .~ , e2 . , ) i s b i v a r i a t e a n d n o r m a l l y d i s t r i b u t e dG I 1 ' -I D ( 0 , H t ) w i t h i ts c o r r e s p o n d i n g c o n d i t io n a l v a r i a n c e c o v a r i a n c e m a t r i x g i v e n b y :

( 2 )

T h e p a r a m e t e r v e c t o r o f th e m e a n r e t u r n e q u a t i o n ( 1 ) i s d e f i n e d b y t h e c o n s ta n tO~ = (O~ , O'2 ) a n d t h e a u t o r e g r e s s i v e t e r m f l = ( i l l , f12 ) , w h i l e t h e p a r a m e t e r m a t r i c e s f o r t h e

v a r i a n c e e q u a t i o n ( 2 ) a r e d e f i n e d a s C o , w h i c h i s r e s t r i c t e d t o b e u p p e r t r i a n g u l a r , a n d t w ou n r e s t ri c t e d m a t r ic e s , A l l a n d G I ~ . T h e r e f o r e , t he se c o n d m o m e n t w i l l t a k e t h e f o l l o w i n g f o r m :

H , = C o C o + ( a l l a 1 2 1 ' I e ~ ' ' - I e l " -l e 2 't - 1 )( a l l a12 /\ a21 a2 2) \ e l, ,_ l e2 , t_ , e2 ,,_1 )~ a z l a22J

\ g : l g z 2 J ~. g z l g z z J ( 3 )

E q u a t i o n ( 2 ) m o d e l s t h e d y n a m i c p r o c e s s o f H t a s a l in e a r f u n c t i o n o f i ts o w n p a s t v a l u e sH t _ 1 a n d p a s t v a l u e s o f t h e s q u a r e d i n n o v a t i o n s e k r _ , e 2,t_ 1 , i n b o t h c a s e s a l l o w i n g f o r o w n -

m a r k e t a n d c r o s s - m a r k e t i n f l u e n c e s i n t h e c o n d i t io n a l v a r i a n c e . T h e i m p o r t a n t f e a t u r e o f t h iss p e c i f ic a t i o n i s t h a t i t a l l o w s t h e c o n d i t i o n a l v a r i a n c e s a n d c o v a r i a n c e s o f th e t w o s e r ie s t o a ff e c te a c h o t h e r , th e r e b y e n a b l i n g o n e t o t e s t t h e n u l l h y p o t h e s i s o f n o v o l a t i l i ty s p i l l o v e r e f f e c t s i n o n eo r e v e n b o t h d i r e c t io n s . F u r t h e r m o r e , i t d o e s n o t r e q u i r e t h e e s t i m a t i o n o f m a n y p a r a m e t e r s ( e i g h tf o r t h e b i v a r ia t e s y s t e m e x c l u d i n g c o n s t a n t , w i t h o u t a n y l o s s o f g e n e r a l i ty ) . E v e n m o r e

2 The m odel is based on the b ivariate GA RCH (1 t)-BEK K representat ion proposed by Engle and K roner (1995).


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380 J O U R N A L O F E C O N O M I C S A N D F I N A N C E 9 Volume 30 9 N u m b e r 3 9 Fal l 200 6importantly, the BEKK model guarantees by construction that the covariance matrices in thesystem are pos itive definite.3

Given a sample of T observations, a vector of unkn own parameters /9 and a 2xl vector ofretur ns r r , the con diti onal density fu nctio n for the model (1) is:

f ( r l , _ l ; a ) = ( 2 x ) - 'H , - 1 / 2 e x p l (4)The log likelihood function

TL : Z l o g f ( r , l l , _ Ot - I

(5 )

is maximized n umeri cally using the Broyden, Fletcher, Goldfarb and Sh anno algorithm to yieldmax imu m likelihood estimates. Standard errors are calculated using the quasi -maxi mumlikelihood methods of Bollerslev and Wooldri dge (1992), wh ich is robust to the distribution of theunder lying residuals.

A n A p p l i c a t io n t o t h e S o u th E a s t A s i a C r i s isIn this section we employ the model described above to investigate the casual relations

between stock returns volatility in the South East Asian market and other main markets. Testingfor cau sality-i n-varian ce is the goal o f our analysis. After describing the data and thebootstrapping LR test procedure, we discuss the results.Data

The data on stock indices are daily (five days per week). The original series were used for theUS and Japan; in addition, two aggregate indices were built, one for Europe (including Italy,France, UK and Ger many ) and the other for South East Asia ( including South Korea, Singapore,Taiwan, Philippines, Malaysia, Thailand, Hong Kong and Indonesia). The indices are weightedaverages, where the weight is the GDP of individual countries converted to US dollars at market

s Note that the BEKK-GARCH specificationemployed in our study implies a joint restriction on the variance andcovariance. This is shown by Darbar and Deb (1997), who employ he Engle and Kroner specification (1995) to examinethe co-movementsof equity returns in four major internationalmarkets. This allows them to decompose the conditionalcovariance into two components. The first, permanent component is the historical (unconditional)mean covariancebetween the returns. A fluctuation of the conditional covariance around this permanent component s the second. Todistinguish between the existence of nonzero permanent and transitory components, they propose the joint restrictionsHo:c12=a12=g12=0. Although we are aware of this issue and of the resulting difficulties in interpreting ests for volatilityspillovers based on joint restrictions,we have decided to use the standard approach found in the literature n order to makeour results comparable o those from previous studies. Furthermore, Darbar and Deb (1997) acknowledge hat their methodsuffers from the "Davies problem" (i.e. identification).Nevertheless, they rely on asymptotic critical values. Studying theproperties of their test by means of bootstrapping echniqueswould undoubtedlybe an interesting esearch topic, but it isbeyond the scope of the present paper.


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JOURNAL OF ECONOMICS AND FINANCE 9 Volume 30 9 Num ber 3 9 Fall 20 06 38 1e x c h a n g e r a t e s 4 , a v e r a g e d o v e r t h e p r e c e d i n g t h r e e y e a r s 5 ( s e e F i g u r e 1 ), o v e r t h e p e r i o d 1 / 1 / 1 9 8 6- 1 1 / 1 0 / 2 0 0 0 , f o r a to t a l o f 3 8 5 5 o b s e r v a t io n s . T h e d a t a w e r e a l l o b t a i n e d f r o m D a t a s t r e a m .

F i g u r e I : S t o c k R e t u r n I n d i c e s

4 -

2 -

0 -

-2 -

-61/0" ~""'""q'i~';h'~........~;8'4~:~........~ , ~ ...........

2 -0 4

-2-4

-6

1 /01 /86 1 1 /0 ~ 1/8 .q ' 9 /0 " ~ 3 3 ' Y/02/97

1 / 0 1 ~

, . ~ ,d .., ,., LL ~ . . . . . . . . . . d . . k , , S

1 /0 ' / 8 6 1 1 /0 1 /8 9 9 /0 1 ~ 3 7 /0 2 /9 7

W e d e f i n e d a i l y r e tu r n s a s l o g a r i t h m i c d i f f er e n c e s o f s t o c k i n d ic e s . T a b l e 2 p r e s e n t s a w i d er a n g e o f d e s c r i p t i v e s t a ti s t ic s f o r t h e f o u r se r i e s u n d e r i n v e s t i g a t i o n , f o r th e f u ll s a m p l e a n d f o rt w o s u b - p e r io d s , n a m e l y t h e p r e - 1 9 9 7 a n d t h e p o s t - 1 9 9 7 p e r i o d . T h e s a m p l e m o m e n t s f o r t h ew h o l e s a m p l e r e t u r n s s h o w h e a v y s k e w n e s s a n d k u r t o s i s ; c o n s e q u e n t l y , J a r q u e - B e r a s t a t i s t i c si n d i c a t e r e j ec t i o n s o f th e n u l l h y p o t h e s i s t h a t s to c k m a r k e t r e t u r n s a r e n o r m a l l y d i s tr i b u te d . T h es t a t i s ti c s i n d i c a t e t h a t t h e n a t u r e o f t h e d a t a i s s u b s t a n t i a l l y d i f f e r e n t i n th e t w o s u b - s a m p l e s .S p e c i f i c a l l y , t h e r e a p p e a r s t o b e a s t a t i s t i c a l l y s i g n i f i c a n t i n c r e a s e i n v o l a t i l i t y s t a r t i n g f r o m t h em i d d l e o f 1 9 9 7 , a s s h o w n b y t e s ts f o r v a r i an c e e q u a l i ty ( s e e T a b l e 1 ). S u c h a n i n c re a s e d o e s n o ta l w a y s c o n v e y u s ef u l i n f o r m a t i o n , g i v e n t h e f a c t t h a t f i n a n c i al m a r k e t s h a v e g e n e r a l l y b e c o m em o r e v o l a t i l e i n r e c e n t y e a r s , a n d i n v e s t o r s h a v e b e c o m e m o r e a c c u s t o m e d t o b i g s w i n g s i n s t o c kp r i c e s . H o w e v e r , i n t h is c a s e t h e h i g h e r v o l a ti li t y o f s t o c k p r i c e s u n d o u b t e d l y c o i n c i d e s w i t h t h eo n s e t o f t h e S o u t h E a s t A s i a n c r i s is , w h i c h b e g a n i n T h a i l a n d i n th e l a te s p r i n g o f 1 9 9 7 w i t hs u s t a i n e d s p e c u l a t i v e a t t a c k s o n t h e l o c a l c u r r e n c y , a n d c o n t i n u e d w i t h i t s f l o t a t i o n i n e a r l y J u l y1 9 9 7 . W i t h in d a y s , s p e c u l a t o r s h a d a t t ac k e d t h e c u r r e n c i e s o f M a l a y s i a , t h e P h i l i p p i n e s a n dI n d o n e s i a . T h e K o r e a n c u r r e n c y w a s a t ta c k e d l a t er o n .

T h e e m p i r i c al d i s t r ib u t i o n s i n f a c t s e e m t o b e d r a m a t i c a l l y i n f l u e n c e d b y t h e b r e a k w h i c ho c c u r r e d i n th e m i d d l e o f 1 9 9 7 . V i s u a l i n s p e c t i o n o f t h e d a t a s u g g e s t s t h a t G A R C H e f f ec t s a rep r e s e n t i n t h e w h o l e s a m p l e a s w e l l a s i n t h e t w o s u b - p e r i o d s . L j u n g - B o x p o r t m a n t e a u s t a t i s t i c s

4 The analysis has also been performed w ith own cu rrency returns. The results have not been reported as they arequalitatively similar and are available from the authors.5 We followed the procedure use d in the Wo rld Economic Outlook Statistical Appendix for constructing aggregateindices.


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38 2 J O U R N A L O F E C O N O M I C S A N D F I N A N C E 9 Vo lume 3 0 9 N u m b e r 3 9 F a l l 2 0 0 6( L B ) f o r s e r ia l c o r r e l a t io n i n th e s t a n d a r d iz e d s q u a r e d r e t u r n s a r e a l s o r e p o r t e d . T h e y c o n f i r m t h a tt h e n ul l h y p o t h e s i s o f w h i t e n o i se r e s i d u a l s c a n e a s i l y b e r e j e c te d . T h e m a g n i t u d e o f t h ea u t o c o r r e l a t i o n v a l u e s s u g g e s t s a n o n - l i n e a r d e p e n d e n c e p a t t e r n ; i n d e e d , t h e s i g n i f i c a n tp e r s i s t e n c e in t h e s q u a r e d r e t u rn s i s c o n s i s t e n t w i t h t h e v o l a t i li t y c l u s t e r i n g c o m m o n l y o b s e r v e d i nf i n a n ci a l s e ri e s. O v e r a l l , t h e s u m m a r y s t a t i s ti c s c o n f i r m t h e w e l l - k n o w n s t y l iz e d f a c t s f o r f i n a n ci a lt ime se r i e s da ta .Resampling LR TestThi s sec t i on repo r t s t he p rocedu re we u se t o ca l cu l a t e t he boo t s t rap ca l i b ra t ed c r i t i ca l va lueso f t h e l ik e l i h o o d r a t i o t e st . W e a s s u m e t h a t u t f o l l o w s a m a r t i n g a l e d i f f e r e n c e , d y n a m i c a l l yh e t e r o s c ed a s t i c p r o c e s s a s in e q u a t io n ( 3 ) . I m p o s i n g z e r o c o n s t r a i n t s o n t h e o f f - d i a g o n a lc o e f f i c i e n t i s e q u i v a l e n t t o t h e n u l l h y p o t h e s i s o f n o G r a n g e r c a u s a l i t y f r o m o n e v a r i a b l e t o t h eo the r and v i cev e rsa . In pa r t i cu l a r , unde r t he nu l l hypo the s i s H 0 : a21 = g21 = 0 , we hav e t ha t h2 ,d o e s n o t G r a n g e r c a u s e h a,, w h e r e a s h a, d o e s c a u s e h 2 . T h e r e f o r e , t h e e q u a t i o n f o r H , w i l l t a k et h e f o l l o w i n g f o r m : 6

'/It C21 2 2 9= + a l l e l , _ l + g H t ~ , -1 (6)2~ 2 , = C ll C l2 + a t l a l 2 e l t - z + a l t a 2 2 e l , - l e 2 t - i + g l l g l 2 ] ~ t - 1 + g l l g e J ~ 2 , - i

2 2 2 2 2h2 t =C22+C22+ a t 2 e l , _ l + 2 a 1 2 a 2 2 e lt _ le 2 ,_ l + a22e2r_, + g ~ 2 h l , _ t + 2 g 1 2 g 2 2 h 1 2 , _ t + g ~ 2 h 2 , _ lT h e l i k e l ih o o d r a t i o te s t, L R h e n c e f o r t h , c o m p a r e s t h e m a x i m u m v a l u e o f t h e l ik e l i h o o d

f u n c t io n u n d e r t h e a s s u m p t i o n t h a t th e n u ll h y p o t h e s i s i s c o r r e c t to t h e m a x i m u m v a l u e o f t h eun res t r i c t ed l i ke l i hood func t ion .

Then , i f t he nu l l i s t rue :L R = - 2 ( L R - I _ v ) (7 )

w h e r e L R a n d L v a r e t h e r e s t ri c te d a n d t h e u n r e s t ri c t e d m a x i m i z e d l i k e li h o o d f u n c t i o nr e s p e c t iv e l y . T h e r e f o r e , u n d e r t h e n u ll h y p o t h e s i s t h e te s t i s a s y m p t o t i c a l l y d i s tr i b u t e d a s a x 2 ( j )w i t h d e g r e e s o f f r e e d o m j e q u a l t o th e n u m b e r o f r es t r ic t io n s . H o w e v e r , n o t e t h at , s in c e t h ed i s t r i bu t ion o f ( r e f : L R t e s t ) u n d e r H 0 w i l l d e p e n d u p o n n u i s a n c e p a r a m e t e r s ( a 2~ a n d g2 ~)w h i c h c a n n o t b e c o n d i t i o n a t e d a w a y , t h e M o n t e C a r l o t e s t m e t h o d d o e s n o t a p p l y e x a c t l y .T h e r e f o r e , in o r d e r t o t a k e i n to a c c o u n t t h e p r e s e n c e o f n u i s a n c e p a r a m e t e r s w e r e s o r t to b o o t s t r a pr e s a m p l i n g . M o r e s p e c i f i c a l l y , w e u s e a b o o t s t r a p p r o c e d u r e a n a l o g o u s t o t h a t d e s c r i b e d i nD a v i s o n a n d H i n k l e y ( 1 9 9 7 , p . 1 4 8) ; o u r r e s u l ts a r e o b t a i n e d f r o m 9 9 9 a r t if i ci a l ti m e s e r ie sg e n e r a t e d f r o m t h e f i t te d m o d e l ( r ef : B E K K R E S T R ) f o r t h e o b s e r v e d s e r ie s o f in t e re s t u s in gi n n o v a t io n s r e s a m p l e d f r o m t h e r e s id u a l s { /~ , } .

6 Similarrestrictions can be imposed n the opposite direction; in that case All and G1t would be up per riangular.


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J O U R N A L O F E C O N O M I C S A N D F I N A N C E 9 V o l u m e 3 0 9 3 9 F a l l 2 0 0 6 3 8 3W e f i n d t h a t t h e L R t e s t h a s f i n i t e - s a m p l e T y p e - I e r r o r p r o b a b i l i t i e s t h a t d o n o t d i f f e r

s i g n i f i c a n t l y f r o m t h e n o m i n a l v a l u e o f 0 . 0 5 w h e n T = ( 8 5 4 , 3 0 0 0 , 3 8 5 4 ) 7 , w i t h e m p i r i c a lr e j e c t i o n f r e q u e n c i e s r e a s o n a b l y c l o se t o t h e c o r r e s p o n d i n g a s y m p t o t i c o n e s . 8

T a b l e 1 : S u mm a r y D e sc r i p ti v e S ta t i s ti c s

C o u n t r yA s i a

E u r o p e

J a p a n

U S A

W h o l e - S a m p l e S u b - s a m p l e sS t a t i s ti c s 1 / 1 / 8 6 - -1 1 / 1 0 / 0 0 1 1 / 8 6 - 1 / 7 / 9 7 2 / 7 / 9 7 - 1 1 / 1 0 / 0 0M e a n 0 . 0 1 6 0 0 . 0 3 0 1 - 0 . 0 3 3 1S t d . d e v . 0 . 5 3 4 6 0 . 4 7 7 6 0 . 6 9 6 5S k e w n e s s - 0 . 2 7 4 4 - 0 . 5 4 5 2 0 . 1 69 3K u r t o s is 9 . 2 9 4 0 9 . 8 0 9 7 . 0 0 4 2LB~_~)~ 6 4 5 . 8 4 * 1 8 7 . 0 1 * 1 1 4 . 4 5 "LB2o)~ 8 6 8 . 4 1 * 2 2 3 . 2 0 * 1 4 7 .2 1 *

J B 6 4 11 * 5 9 4 5 " 5 7 5 *M e a n 0 . 0 1 5 4 0 + 0 14 8 0 . 0 t 8 2S t d . d e v . 0 . 4 2 7 8 0 . 4 0 6 2 0 . 4 9 6 6S k e w n e s s - 1 . 0 4 3 - 1 . 4 4 5 6 - 0 . 2 3 7 8K u r t o s i s 1 4 . 34 3 2 0 . 1 8 7 3 . 8 9 2LB~)_ 1 7 8 . 5 9 " 1 2 8 . 1 1 * 6 3 . 7 7 0 *LB21o) 2 0 9 . 3 6 * 1 4 3 . 0 4 * 1 2 1 . 41 *

J B 2 1 3 6 3 " 3 7 9 7 3 * 3 6*M e a n 0 . 0 0 9 1 0 . 0 1 4 3 - 0 . 0 1 0 3S t d . d e v . 0 . 6 8 2 6 0 . 6 4 5 4 0 . 8 0 0 3S k e w n e s s - 0 . 0 3 7 9 - 0 . 3 3 8 8 0 . 5 43 1K u r t o s i s 1 1 . 3 1 7 1 3 . 7 4 6 6 . 6 8 6 9--LB25) 2 2 3 . 0 4 * 4 8 1 . 9 6 * 4 0 . 6 8 6 *LB2o)~ 2 7 8 . 1 7 " 6 3 6 . 7 9 * 5 4 . 3 1 2 "

J B 1 1 1 1 0 " 1 4 4 9 4 * 5 2 6 *M e a n 0 . 0 2 13 0 . 0 2 0 8 0 . 0 2 33S t d . d e v . 0 . 4 52 1 0 . 4 2 4 7 0 . 5 3 7 7S k e w n e s s - 3 . 12 1 - 4 . 6 2 6 3 - 0 . 3 7 41K u r t o s i s 6 9 . 1 1 6 1 0 9 . 2 0 6 . 6 8 6 6LB,_s)__ 2 3 1 . 8 5 * 1 8 0 . 0 7 * 5 7 . 6 3 3 *L B ~ o- 2 4 5 . 6 5 * 1 8 9 . 9 7 " 8 6 . 1 6 8 "

J B 7 0 8 2 3 * 1 4 2 0 6 2 " 5 0 4 *N o t e s : The s ta r ind ica tes re jec t ion a t the 5% level . LB(m and LBoo) a re respec t ive ly the L jung-Box test o f s ign i f icanceof au to corre la t ion s of f ive and ten lags in the s tandard ized squared residuals . Var ian ce equa l i ty tes ts have been carr iedout (L evene , 1960) wi th the nul l hypoth esis of equa l pre -c r is is and post -c r is is var iance be ing re jec ted in a ll four cases .Th e tests y ie lded va lues o f 18 .48 , 7 .78 , 11 .43 and 8 .87 respect ive ly , a l l o f wh ich a re b igge r than the corresp onding F (1 ,3852 ) c r i t ica l va lues.

7 The se a re th e sam ple s izes correspo nding to the pre - and post -cr ises sam ples respec t ive ly .s Since the percen t re jec t ions a t the 0 .01 , 0 .05 and 0 .10 s igni f icance leve ls a re qua l i ta t ive ly simi la r , w e focus o urd iscu ssion o n the proper t ies of 0 .05- leve l tes t.


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38 4 JOURNAL OF ECONOMICS AND FINAN CE 9 Volume 30 9 Numb er 3 9 Fall 2006

T a b l e 2 : B o o t s t ra p p ed L i k e l ih o o d R a t i o T es t

Whole sampleT = 3 8 5 4

E u r o p e a n d U S A a n d J a p a n a n dE a s t A s i a E a s t A s i a E a s t A s i a

13.15 14.77 19.01

Pre-crisis sample 16.22 38 .64 15 .69T = 3 0 0 0Post-crisis sample 6.63 14.77 6.31T = 8 5 4Notes: Bootstrapped ikelihood ratio Typ e-Ierror probab ilityof 0.05-Level are reported.

E m p i r i c a l R e s u l t sT h e e s t i m a t e d c o n d i t i o n a l v a r i a n c e s w i t h a s s o c i a t e d r o b u s t s t a n d a r d e r r o r s a n d l i k e l i h o o d

f u n c t io n v a l u e s fo r th e S o u t h E a s t A s i a n a n d th e E u r o p e a n , U S a n d J a p a n e s e s t o c k m a r k e t r e t u r n sa re p re sen t ed i n Tab l e s 3 , 4 an d 5 re sp ec t i v e ly .

F o r e a c h m o d e l , t h e A k a i k e , B a y e s i a n a n d H a n n a n - Q u i n n i n f o r m a t i o n c r i t e r i a h a v e b e e ne m p l o y e d t o d e t e r m i n e t h e c o n d i t i o n a l v a r i a n c e l a g l e n g t h s . T h e s e s u g g e s t t h a t a G A R C H ( 1 , 1 ) -B E K K s p e c i f i c a ti o n i s a p p r o p r i a t e f o r t h e c o n d i t i o n a l v a r i a n c e . H y p o t h e s i s t e s t in g i s p e r f o r m e d o nth e mo d e l s u s in g t h e l i k e l i h o o d ra t i o t e s t , an d co mp ar in g t h e t e s t s t a t i s t i c s wi th t h e emp i r i ca lc r i t i c a l v a l u e s r e p o r t e d i n T a b l e 1 . W e c a r r y o u t t e s t s f o r c a u s a l i t y - i n - v a r i a n c e f o r e a c h m o d e l ,a l t e rn a t i v e ly co n s t ra in in g t h e ma t r i ce s A~] a n d G l l t o b e u p p e r t r i a n g u l a r a n d l o w e r t r i a n g u l a r ,t h e r e b y a l lo w i n g f o r c a u s a l i t y o n l y i n o n e d i r e c ti o n a t a t im e . W e r e p o r t t h e L R s t at is t ic s a n d t h ea s s o c i a te d p - v a l u e s o n l y w h e n t h e re s t ri c ti o n i s a c c e p t e d .

T h e n u l l h y p o t h e s i s o f u n i d i r e c t i o n a l c r o s s - m a r k e t s p i l l o v e r s i s r e j e c t e d w h e n t h e f u l l s a m p l eo r t h e p re -1 9 9 7 p e r io d a re co n s id e red , b u t i t c an n o t b e re j ec t ed i n t h e p o s t -1 9 9 7 p e r io d fo r a l l t h eth ree mo d e l s . Th e p a t t e rn s i n t h e co n d i t i o n a l v a r i an ce co e f f i c i en t s a re n o t su b s t an t i a l l y d i f fe ren tac ro ss mo d e l s . Th e e s t im a te s a re i n m o s t ca se s s t a t i s t ica l l y s i g n i f i can t . 9. In o rd e r t o t e s t t h ea d e q u a c y o f th e m o d e l s , L j u n g - B o x p o r t m a n t e a u t e s ts ( L B ) w e r e p e r f o r m e d o n s t a n da r d iz e d a n ds t a n d a r d i z e d s q u a r e d r e s i d u a l s . O v e r a l l t h e r e s u l t s i n d i c a t e t h a t t h e G A R C H ( 1 , 1 ) s p e c i f i c a t i o ncap tu re s sa t i s fac to r i l y t h e p e rs i s t en ce i n sq u a red re tu rn s i n t h e se r i e s , wi th t h e n u l l h y p o th es i s o fn o a u t o c o r r e l a ti o n b e i n g r e j e c t e d i n j u s t o n e c a s e a t t h e f i v e p e r c e n t l e v e l . T h e c o e f f i c i e n t v a l u e sf o r o w n - m a r k e t v o l a t i li t i e s i n d ic a t e h i g h p e r s i s t e n c e i n t h e s t o c k r e t u rn s , w i t h c o e f f i c i e n t e s t i m a t e st h a t a r e al l b i g g e r th a n 0 . 9 . I n t e r e s ti n g l y , t h o u g h , i n t h e p r e - c r is i s s a m p l e t h e G A R C H p a r a m e t e r sa re l e s s p e rs i s t en t i n a l l t h e mo d e l s , wi th v a lu es ran g in g f ro m 0 .7 7 t o 0 .9 3 .

9 The covariancestationarycondition is satisfiedby all the estimated models.


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J O U R N A L O F E C O N O M I C S A N D F I N A N C E 9 V o l u m e 3 0 9 N u m b e r 3 9 F a l l 2 0 0 6Table 3: Estimate d GAR CH (1,1) Models for the Euro pe a nd South East Asia Stock

R e t u r n s

385

Whole sample1/l/86- 11/10/00 Pre-crisis sample1/1/86- 1/7/97 Post-crisis sample2/7/97 - 11/10/00Parameters Coef, S.E, Coef. S.E. Coes S.E.

.0245 .0056 ,0177 .0068 .0298 .0145fl l ,0577 .0777 ,0790 .0181 .0201 ,0207~2 .0315 .0054 .0300 ,0070 -,0211 .0208f12 .1067 .0567 .0487 ,0308 ,2748 .0319Cll -,0573 .0125 -.1013 .0243 .0673 ,0032C12 -.0424 .0104 -,0159 .0400 .0151 .0071C22 ,0607 ,0149 -.0411 .0249 .1657 .0074g l l ,9979 .0149 .7915 .0390 -.9635 .0010g12 .4700 ,0824 -.7583 .1195g21 -.1670 ,0635 -.1616 .0540 .0149 .0050g22 .9879 ,0129 .8861 .0659 -.8831 .0038a l l .2391 .0329 .2002 .0460 .2316 .0058a12 .0962 .0381 .1044 .0946a21 .0048 ,0260 .1997 .0609 .1658 .0174a2 2 .2665 ,0363 .3242 .0307 .3386 ,0t06LogLik 2737.021 2569.826 249.486LR Test 6.36p-vMue (.0415)

L B E ( IO ) 4.5905 8,609 3.60882L B E ( I O ) 13,012 18.389 14.691

L B A ( I O ) 3.2374 6.0582 4,2074

LBA2(10) 3.8243 6,6242 10.302No tes : Quasi maximum ikelihood standard errors (S,E.) based on Bollerslev and Wooldridge (1992) are reported. A *indicates rejectionat the 5% level, LR test p-valuesare in parentheses. LB(10) and l.,BZ(10) are respectively he Ljung-Box test of significance of autocorrelations of ten lags in the standardized and standardized squared residuals. Thecovariance stationary condition is al so satisfied by all the estimated models, all the eigenvalues ofA11 | AI 1 + GI 1 G11 being less than one in modulus.


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3 8 6 J O U R N A L O F E C O N O M I C S A N D F I N A N C E 9 V o l u m e 3 0 9 N u m b e r 3 9 F a l l 2 0 0 6

T a b l e 4: E s t i m a t e d G A R C H ( 1 , 1) M o d e l s f o r t h e U S A a n d S o u t h E a s t A s i a S t o ck R e t u r n sW h o l e s a m p le

1/1/86 - 11/10/00Pre-crisis s a m p l e

1 /1 /86 - 1 /7 /97Post-crisis s a m p l e2/7/97 - 11/10/00

Param eters Coef . S .E. Coef . S .E. Coef . S ,E..0261 .0052 .0234 .0068 .0227al

f l l .0343 .0171 .0471 .0234 .0353O~ .0301 .0069 .0298 .0102 - .0176f12 .1041 .0186 .0555 .0171 .2705C l l - .0447 . 0009 . 0315 . 0252 . 1294C12 - .0067 .0019 - .0852 .0474 -.0058C 22 .0554 .0021 .0000 .0974 .1672g l l . 9666 .0003 .9272 .0226 .9402g1 2 .0168 .0007 .383 2 .0134g2 1 - .0112 .0004 - .2642 .0103 .0045g22 . 9544 .0006 .8882 .0414 .9023a l l . 2320 .0015 .1961 .0839 - .2330a1 2 - .1016 .0033 - .0881 .0262a2 1 .0473 .0019 .0631 .0347 .0531a2 2 .2779 .0028 .2264 .0713 .3630

Lo gL ik 2757 . 107 2683 . 087 121. 562LR Te s t 7 .1p - v ~ u e ( . 0 2 8 7 )

7 . 657 6 . 297 6 . 6488L S u ( 5 )2 22.649* 15.276 15.445L B u o 0

7.9737 8 .114 9 .3755L B A ( 5 )9 ( 9 .1776 15.795 9 .5730

L B 10)

.0167

.0394

.0211

.0458

.0417

.0242

.0561

.0319

.0011

.0515

.0616

.0149

.0905

Notes: See Notes for Table 3.


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J O U R N A L O F E C O N O M I C S A N D F I N A N C E 9 V o l u m e 3 0 9 N u m b e r 3 9 F a l l 2 0 0 6 387T a b l e 5 : E s ti m a t e d G A R C I t ( 1 ,1 ) M o d e l s fo r t h e J a p a n e s e a n d S o u t h E a s t A s i a S t o c k R e t u r n s

W h o l e s a m p le1/1 /86 - 11 /10 /00

Pre -c r i s i s s ample1 / 1 / 8 6 - t / 7 / 9 7 Pos t -c r i s i s s ample2/7 /97 - 11 /10 /00

P a r a m e t e r s C oe f . S . E . C oe f . S . E . C oe f . S . E .~ 1 . 0289 . 0150 . 0332 . 0120 . 0112 . 0209

~ 2 .0341 . 0110 . 0406 . 0085 - . 0060 . 0220&C11 .1036 .0213 .1135 .0180 .0801 .042 6C 12 . 0432 . 1254 . 0780 . 0573 . 0049 . 0666C 22 . 0778 . 0488 . 0766 . 0116 . 1454 . 0895

.9503 .0153 .9382 .0162 .9659 .0091g l l- .0004 .0115 - .0101 .0071g 1 2- . 0407 . 1641 - . 0656 . 0699 . 0499 . 0473g 2 1

g22 . 9308 . 1127 . 9128 . 0542 . 9168 . 0820. 2724 . 0376 . 3049 . 0374 - . 1586 . 0912

a l l - . 0052 .0173 . 0157 . 0148a12. 1206 . 2928 . 1315 . 1120 . 0890 . 0599a21. 3357 . 2305 . 3454 . 0987 . 3509 . 1521a 2 2

L o ~ L i k 1 2 2 2 .2 7 2 1 0 3 3 .9 6 7 t 6 5 . 9 3 0L R T e s tp - v a l u eL B j ( I O ) 0 . 7 7 5 4 0 . 6 1 3 4 7 . 1 9 9 7

2 1 . 8023 2 . 0050 10 . 336L B j ( I O )L B A ( I O ) 5.48 50 10 .295 3 .7501

( 18 .126 18 .639 12 .848L B 10)Notes : See N otes for Table 3.


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388 JOURNAL OF ECONOMICS AND FINANCE 9 Volume 30 o Num ber 3 9 Fall 2006C r os s - m a r ke t vo l a t i l i ty de pe nd e nc e va r i e s i n m a g n i t ude a nd s i gn a c r o s s m a r ke t s . W e f i nd

f e e dba c ks i n va r i a nc e in bo t h d i r e c ti ons i n a ll t he m od e l s ove r the w h o l e s a m p l e a s w e l l a s i n t hep r e - c ri s is s a m p l e , a r e s u l t w h i c h - is c ons i s t en t w i t h t he g r ow i ng de g r e e o f i n t e g r a ti on o f f ina nc i a lm a r ke t s o ve r t he la s t t w o de c a de s . H ow e ve r , t he r e a r e a s ym m e t r i e s i n v o l a t i li t y s p il l ove rs a c r o s sm a r ke t s . I n pa r t ic u l a r, t he S ou t h E a s t A s i a n c o nd i t i ona l va r i a nc e de pe nd s pos i t i ve ly on s ho c kso r i g i na t ing i n the E u r op e a n m a r ke ts , w h i l e i nnov a t i ons i n t he U S m a r ke t de c r e a s e t he S ou t h E a s tA s i a n c ond i t i ona l va r i a nc e . S hoc ks w h i c h oc c u r r e d i n t he J a pa ne s e m a r ke t ha ve a pos i t i ve e f f e c ton the South Eas t As ian condi t iona l va r iance ove r the fu l l s ample , whi le in the pre -c r i s i s pe r iodt he i r i n f l ue nc e i s ne ga t i ve a nd s m a l l e r . T he pos i t i ve s i gn f ound i n t he c r o s s - m a r ke t c ond i t i ona lva r i a nc e s ugge s ts t ha t t he vo l a t i l it y o f S ou t h E a s t A s i a n s t oc k r e tu r n s ha s a pos i t i ve c l u s t e r e f f e c ton t he o t he r m a r ke t s . I n pa r t ic u l a r, pos i t ive S ou t h E a s t A s i a n s hoc ks ha v e a s t r onge r i n f l ue nc e i nt he p r e -c r i si s pe r iod c o m p a r e d w i th t he w ho l e s a m p l e . O n t he o t he r ha nd , i n t he pos t- c r is i s s a m p l ec r os s - m a r ke t de pe nde nc e i s j u s t i n one d i r e c t i on , w i t h t he S ou t h E a s t A s i a n m a r ke t a f f e c t i ngpos i t i ve l y t he E u r ope a n a nd U S m a r ke ts . T he b i d i r e c t iona l s p i l love r f ound i n t he c a s e o f J a pa n i snot surpr i s ing , a s the co l lapse of some mid-s ize Japan ese banks w i th the r e su l t ing f inan c ia lp r ob l e m s a nd h i ghe r vo l a t i l i ty in t he J a pa ne se m a r ke t s w e r e pos s i b l y e xpe c t e d a p r io r i to ha ve a nimpac t on vola t i l i ty in the o the r As ian marke t s . The LR s ta t i s t i c s a s soc ia ted wi th the nul l o f ze roc r os s - m a r ke t vo l a t i l i t y s p i l l ove r s f r om t he U S , E u r ope a n , a nd J a pa ne s e t o t he S ou t h E a s t A s i a nm a r ke t c a nno t be r e je c t e d . T he x 2 ( j ) s t a ti s ti c s y i e l de d va l ue s o f 6 .36 , 7 . 1 a nd 8 . 1 , al l o f w h i c hha ve c o r r e s pond i ng p - va l u e s b i gge r tha n t he c o r r e s pond i ng boo t s t r a ppe d c r i t ic a l va l ue s .F u r t he r m o r e , t he pos i t i ve s i gn s ugge s ts t ha t f i na nc i a l t u r bu l e nc e , r e f le c t e d i n h i ghe r s t oc k r e t u r n svo l a t il i ty , ha s a pos i t i ve c l u s t e r e f f e c t on t he o t he r m a r ke t s . O ur f i nd i ngs a r e c ons i s t e n t w i t h t hos eo f o t he r s tud i e s t a k i ng a s i m i l ar a pp r oa c h , s uc h a s C he ung e t al. ( 2002 ) , w ho f ound i n t e r a c t i onsbe tween the US, the Japan and four Eas t As ian marke t s . In pa r t i cu la r , our ana lys i s a l so ind ica te st ha t t he de ve l ope d m a r ke t s w e r e G r a nge r - c a us e d by t he S ou t h E a s t A s i a n one s du r i ng t he c r i s i spe r i od , e ve n t hough w e e m p l oy a gg r e gat e i nd i c e s f o r t he E u r ope a n a nd S ou t h E a s t A s ia n s t o c km a r ke t s , r a the r t ha n i nd i c e s f o r i nd i v idua l c oun t r i e s a s i n t he a f o r e m e n t i one d s t udy .

Conc l u s i o n s

I n t h i s pa pe r w e ha ve e xa m i ne d vo l a t i l i t y t r a ns m i s s i on a c r o s s e m e r g i ng a nd de ve l ope d s t oc km a r ke t s , w h i c h , w e h a ve a r gue d , i s o f c r uc i a l i m p or t a nc e f o r und e r s t a nd i ng ho w f i na nc i a l c r i s e ss p r e a d ( c on t a g i on e f f e c t s pos s ib l y r e fl e c ti ng t he " he r d i ng " be ha v i ou r o f i nve s t o r s , as po i n t e d ou tby K a m i ns ky a nd S c hm uk l e r , 1999 ) , a nd ha s no t be e n du l y i nve s t i ga t e d . I n pa r t i c u l a r , w e ha vea na l y s e d t he e f f e c ts o f the 1997 S ou t h E a s t A s i a c r is i s on o t he r m a j o r s t oc k m a r ke ts . I n l i ne w i t ho t h e r p a p e rs , w e h a v e a d o p t e d a B E K K r e p r e s e n t a t io n o f a b i v a ri at e G A R C H m o d e l ( s e e E n g l ea nd K r one r , 1995 ) . H ow e ve r , w e ha ve i m pr ove d on e a r l i e r c on t r i bu t i ons , w h i c h ha d ove r l ooke df i n it e s a m p l e i s sue s , by c ons t r uc t i ng a pp r op r i a t e c on f i de nc e in t e r va ls f o r t he L R t e s t by m e a n s o fboots t r apping in orde r to t e s t for causa l i ty - in-va r iance , the reby obta in ing more re l i ab le s ta t i s t i ca lr e s u lt s . T he a dop t e d f r a m e w or k ha s be e n a pp l i e d t o da i l y da t a on s t oc k r e t u r n s . I n pa r t ic u l a r, t h r e epa i r w i s e m ode l s ha ve be e n e s t i m a t e d p r ov i d i ng s om e e m p i r i c a l e v i de nc e on t he t r a ns m i s s i on o fvo l a t il i ty a c ro s s U S , E u r op e a n , J a pa ne s e a nd S ou t h E a s t A s i an f i na nc i a l m a r ke t s .T he e m p i r i ca l r e s u l ts c a n b e s um m a r i se d a s f o l l ow s . T h e r e i s e v i d e nc e o f vo l a ti l it y s p i l l ove r sin a l l c a ses , though i t i s a l so c lea r tha t the re a re s igni f i cant d i f f e rences in the na ture of thet r a ns m i s s i on m e c ha n i s m s ( a nd t he s i z e o f t he s hoc ks ) . M or e i n de t a i l , t he r e a ppe a r t o beb i d i r e c t i ona l f e e dba c ks i n t he s e c ond m om e n t ove r t he w ho l e s a m p l e a s w e l l a s t he p r e - c r i s i ss a m p l e , t hough t he dy na m i c s o f t he c ond i t i ona l vo l a t il i ti e s d if f e r. O n t he o t he r ha nd , c a us a l i t yl i nks i n t he va r i a nc e be c om e un i d i r e c t i ona l f o l l ow i ng t he ons e t o f t he c r i s i s , r unn i ng f r om t hemarke t s in turmoi l to the o the r s . This sugges t s tha t an impor tan t f ea ture of f inanc ia l c r i se s i s tha t ,a f t e r the c r i s is ha s s p r e a d i n t e rna t iona l l y , t he c oun t r i e s o r i g i na l l y a f f e c t e d be c om e un r e s pons i ve t o


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JOURNAL OF ECONOMICS AND F INANCE 9 Volume 30 9 Number 3 9 Fall 2006 389de ve l op m e n t s in o t he r f i na nc i a l m a r ke ts . T h i s i s c on s i s te n t w i t h the i de a t ha t , t hough t he bu i l d - upi n vu l ne r a b i l i ty ( due t o f i na nc i a l w e a kne s s e s) i n s uc h c ou n t r i e s m i gh t be g r a dua l ( s e e A l ba e t a l . ,1999 ) , t he p r e c i p i ta t i on o f t he c r i s is r e p r e se n t s a r e g i m e s w i t c h , w i t h a j um p f r om one e qu i l i b r i umt o a no t he r ( s e e J e a nne a nd M a s s on , 2000 ) . I n o t he r w or ds , i t g i ve s s uppo r t t o c r i s i s - c o n t i n g e n tm ode l s , i n w h i c h t he be ha v i ou r o f i nve s t o r s , a nd c ons e que n t l y t he t r a ns m i s s i on m e c ha n i s m ,c ha nge a f t e r a s hoc k h i t s t he e c onom y . T h i s i s i n c on t r a s t t o n o n - c r i s i s - c o n t i n g e n t m ode l s , i nw h i c h s hoc ks a re p r opa g a t e d t h r ough s t ab l e l inka ge s ( e .g . t ra de l inks - s e e G l i c k a nd R os e , 1999 ) ,a nd t he t r a ns m i s s i on m e c ha n i s m i s t he s a m e i n c r i s i s a nd t r a nqu i l pe r i ods . I t a l s o s ugge s t s t ha ti n t e r na t i ona l d i ve r s i f i c a t i on i n r e duc i ng po r t f o l i o r i s k du r i ng a c r i s i s w i l l be on l y r e l a t i ve l ye f fec t iv e i f i t i s based on pre -c r i s i s e s t ima te s . F ina l ly , i t c an be seen a s an a rgum ent fo r IM Fi n t e r ve n t i ons a nd ba i l - ou t s , t hough t he r e i s, o f c ou r s e , a m or a l ha z a r d p r ob l e m ( s e e F o r be s a n dR i gob on , 2002 , f o r m o r e de t a il s ).

A s a na t u r al e x t e n s i on o f t he b i var i a te a na l y s i s c ondu c t e d i n the p r e s e n t pa pe r , i t w ou l d beus e f u l t o e s ti m a t e a k - va r ia t e m od e l a nd t o e xa m i ne vo l a t i li t y s p i l l ove r s a m ong a ll f ou r m a r ke t s ;a l s o , r e cu r s i ve t e c hn i que s c ou l d be u s e d f o r e a c h m a r ke t t o de t e c t t he e xa c t t i m i ng o f a ny b r e a ks .T h i s w i l l be the ob j e c t o f f u t u r e w or k .ReferencesAlba , P . , A . Bh a t tacha ry a , S . C laessens , L . Hern and ez , and S. Gh osh . 1 998. "Vo la t i l i ty and

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