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Forec as t-error-b as ¯s alpolc y ru esf ed c i l or m ac roec on i m od el¤ om c s J avi J .P ¶rez er e P au eb ert lHi E u ropeanCen tralB an k Draf verson{ c omm en elome t i tsw c J u y 4 ,2 0 0 1 l A bst a t rc Int ispa r epr se tamo e - se h pe ,w e n d lba dme h df rimpl me t ge o e o s to o e n in nd g n u ¯ a ul s f rst c st sc lr e o o ha icma r e o o c o c n micmo e s.T he me h d l g is ba d o dl t o oo y se n t est bil ya l sis o hemo la a d it t e¯ a u h r yr a t go h a it nay ft de th n ,w h h sc la t o it e c in n t e ba o x c a io e r r o g n s in t e mo e ,w h impl ity c pt e h sis fe pe t t n r o s fa e t h d l hic ic l a ur t ee e to o h st l me t int emo e .T h ul c ie e t ed a im o h ® c fst c a icee n s h dl er ea h v s h u la f impo gsov n yo t e ¯ a c o n g ne a in sin l e c n h sc lse t ra d e r t gast t - o t e ta j st a e c n ing n d u me tt o k inaf r a d l o in r me o kc n e tw ht epr pe t s o n osh c s o w r - o k gf a w r o sist n it h o rie f t emo e .U p t o ,¯ a u e inl a gl r e sc l h dl on w sc lr l s e din a g - aema r e o o c o c n micf r c st oe a in gmo e s h v d l a ebe n impo de o e o sl ,a d int is se e se x g n u y n h nsea en tn c ssa il r o ee ry c mpa ibl w h t e f r a io o t rse t r o h se mo e s.A n e a e o t e it h o mul t n fo he c o s ft e dl x mpl o h ft ede iv t npr c d r ,in l d gso r a io o e u e cu in meilust a iv e ls,is pr v du g l r t er su t o ide sin asmalc l a e ma r l aibr t d c omo l de. T h ie s e pr sse ev w x e dint is pa ra et o ft ea t o s a dd o e e r yr ° e tt o f h pe r h seo h u h r n on tn c ssa il e c h seo t eEu o a h r pe nCe t a a ECB ) T h u h r w u dl et h n n r lB nk( . ea t o s o l ik ot a kM . t n r ,P. u - h n , Ca e a o Co rT ima n J M a¶,P. c d m,F. ra d . r u h . u u a - V id l l n it min rpa t ipa t rn ³ M A a O l n i,R St a c ,M T j l ,J. P. a,ao gw hse a r ic n s a h r B a c ' aiaW o k o o ubl tt e3 d n ad It l r sh p nP icFina c ,a da h n e n tt eFisc lP oic s D iv no h a l ie isio ft eECB , f rh l u isc ssio s a d c mme t o e pf ld u n n o n s.A n r ma ge r r a e o o r t e soe r spo sibil y o y e inin ro s r fc u se h l e n it f t ea t o s.Co t c e a s { e ma d r ss:j v rpe e e b. t u .ie r@ e b. t h uh r n a td t il - ila d e a ie . r z@ c in ;pa lh be t c in ¤ 1 1 I trod u ti n c on Inl r e sc l a g - aema r e o o c o c n micf r c st o e a ingmo e s,in l din h seu dbyl a in d l cu gt o se ed g in e n t n lin it t n h t r a io a st u io s,t emo e l go h sc lse t rin ov s so d lin ft e¯ a c o v l e met peo y f ¯ a l sur r l .T h r l ,o sc lr a t n f n t n,se v s a du lpu po . sc lco e u e is u e r¯ a e c io u c io re a r se Fir , a d mo st n stimpo t n l , it incusio is u d t g n r t sov nc f rt ra ty s l n se o e e a e l e y o he ¯ a c o ,g a a t e gt a h in e t mpo a dg tc n r in ft e g v sc lse t r u r n e in h tt e t re r lbu e o st a to h o en n r me tis sa is¯ d a d g n r t gmo lco r .T h tis,t e po t e n e e a in de l su e a h ssibil y o n it fa u st bl re pl siv n a eo x o epa h f r¯ a a ia e suc a t e g v r me td btr t t o sc lv r bl s h s h o e n n e a io is r e o t n a ar su ta e t in t emo la ew l gt ul d u ,a d s e l g n s h de r ilin ohod pu icd bt l bl e . Se o ,t er ee c nd h ul mbo ie so d s mebe v ur le e n s r g r ingt ha io a l me t e a d hein e t mpo t re r lbe v uro o e n n s { a a ha io fg v r me t ndho d u me t o sc lv r bl s a ema wa j st n s f¯ a a ia e r de v µv t e is- - is h irst a a e dyst t au s in t a eo o k o l yc a g s.Int is a ev l e hef c fsh c s rpoic h n e h se se het n ,t imepa ho d u me t in¯ a n t e a ia e int t fa j st n s sc la do h rv r bl s hemo e r d la e in u nc d byt o mu a io o he¯ a u e ° e e hef r l t n ft sc lr l . T h o mu a io ft e u e a n a ef r l t no h ser l sc ne t ilsig i¯ a te o micc nse u nc sf r n c n c no o qe e o t er suls o h e t fmo e d lsimu a io s a o e a s.T h l t n ndf r c st espe i¯ a io a dc l a io c c t n n aibr t n o fa¯ a u e c n a e tn to l ¯ a l y v r bl s,bu l e e o o sc lr l a ® c o n y sc lpoic a ia e tasok y c n mic a d¯ a c lv r bl s,g e ha g n s' e isio s( h td t r et lo a io n n n ia a ia e iv nt ta e t d c n t a e e min heal c t n o u pu )de n t so e t n n t f ur t fo t t pe d o me x e to he ut e ime pa h o sc lv r bl s. t s f¯ a a ia e T h f r c st a d poic simu a io s ba d o t e mo e s a e u d in ma y e oe a s n ly lt n se n h se d l r se n in a c s a a impo t n pu t st n e s n r a tin tin opoic d c n ma ing l y e isio - k .Co se u n l ,t n q e ty he f r l t n a d impl me t t n o ¯ a r l s h s w e r n in impl a io s. o mu a io n e n a io f sc l u e a id - a g g ic t n Y e ,t it r t r t hel e a u esuro n r u dingt ef r l t no sc lr l sh st u a e e e h o mu a io f¯ a u e a h sf rr c iv d c n e a yl ss a t n io h nt ec re n in it r t eo o sid r bl e t e t nt a h o r spo d gl e a ur nmo e a ypoic ntr ly r l s ( e o st nc ,M c lu u e se ,f rin a e Cal m,1 999) . In g n r l h e ist g¯ a u e e o e in l a in e e a,t e x in sc lr l s mpl y d e d gma r e o o c o c n micf r oe c st gmo e s a e impo d e o e usl ,a d in ov ba k a d l o ingg v r a in dl r se x g no y n v l e c w r -o k o e nme t e e w e ho h l n s v n h n use ods,¯ms a d t emo e a ya ho it r r n h n t r ut r ya emo e l d in d le a o imisin o w r - o k gf a w r .T he r l s use in pr c ic a e q it n pt gf r a d l o in r me o k ue d at e r u e d e se in spe i¯ a io , a d so r c n u ie h v f u d t r u h st nd r iv r c ct n n me e e tst d s a e o n h o g a a dise dsimu a io s t tt ev r u spe i¯ a io s a dc l a io ft ser l s c n l t n ha h a io s c c t n n aibr t no he u e a l a t id l iv r e tr su t a sh w o x mpl ,in M it h l ta. 20 0 0 ) e d ow e yd e g n e ls s o n,f re a e c e le l ( , B r a ta d Z ha 1 996aa d 1 996b)a d Ch c e l ( 997 . yn n ng( n n ur h ta. 1 ) In mo e s w h o imisin f r a d-o k g a e t t e in e t mpo a sc l d l it pt g o w r l o in g n s, h t re r l¯ a r l sh u d in pr c e aso be mo e l d in a f r a d l o ing w y Id al , it ue o l in ipl l d le o w r -o k a . e ly sh u d in l d e pe t t n o ut e v l s o e e a tv r bl s a d,a dit no l cu e x c a io s ff ur aue fr l v n a ia e n d io al ,poic r a t n t h d e e tsh c s a e t gt e e o o .Su h a r l ly l y e c io s ot e i® r n o k ® c in h c n my c ue w u d a un o so c mbin t n ( it e in a rn n in a )o nd g n u o l mo tt me o a io e h rl e ro o l e r fe o e o s a d e o e o s v r bl s in t emo e . n x g n u a ia e h dl In t is pa rw sh w t a f rmo lco r , t r l v n ¯ a r l c n h pe e o h t o de l su e he ee a t sc l u e a be spe i¯ d a d/ rc l a e e do e o sl .Spe i¯ al ,w sho c e n o aibr t d n g n u y c c ly e who wast t ae c n in e tpoic u er l t g¯ a st u n s t o t gn l yr l e a in sc lin r me t odi® r n o k a e t gt e e tsh c s ® c in he eo o c n mya de pe t t n o u u ed v l pme t ft ee o o n x c a io s ff t r e e o n so h c n myc nbed r e a e iv d 2 o h nt eba o h x in tu o sis ft ee ist gse - p famo e .Int ea n eo n a t emo e dl h bse c fa c iv nt r u h r ymo t gsh c s t e ,a is int ec seo a ya t o it ne isin o k od bt s h a fmo stin u r l d d st iaise c u t ie o n r s,a¯ a u h r y c n be t o g to s r a t gt n v t n a e t sc la t o it a h u h fa e c in oin o a io s ® c in e h o g t e a j st n fbu e a yit ms in o de og a a t e de gd btt r u h h d u me to dg t r e r rt u r n e bt su a a it ,w ic e t te st in bil y h hse ms o¯ mpir a v e c B o n 998 a dKil t ic , ic le id n e( h ,1 n pa r k 20 0 1 ) . B yu gst n a d st bil ya ay t o yf rr t n le pe t t ns mo e s, sin a d r a it n l sis he r o a io a x c a io dl a pr se t d in B l n ha d a d Kh n ( 981 )o s e ne ac r n a 1 rSims ( 0 0 ) e sh wh wsuc 20 ,w o o h ar e c n be d r e ,a d h wt o st u tito t e ba o h e pe t t n ul a e iv d n o oc n r c n h sis ft e x c a io s e r r o a e t w h t e mo l T h st t - o t e t a d f r a d-o k g r o s f g n s it in h de. e a e c n ing n n o w r l o in n t r o h r l impl s t a dj me tu e he ide t e ¯ a ul do s a u e ft e u e ie h ta ust n nd rt n i¯ d sc lr e e n tde nd o mo e n s in so o pe n v me t mee o e o s ¯ a a g tv r bl isc n e t d x g n u sc lt r e a ia ed o n c e fo t r m hespe i¯ a io c c t nmo la a d tr t ritis af n t no h ur e o de th n ,bu a he u c io ft eso c s f u c ra t ® c in h mo e c n myu de ud .In t is w y her spo n e t in ya e t gt e d le o o n rst y h a ,t e nse o he¯ a u h r yis d pe d n n t e so r eo h ft sc la t o it e n e to h u c ft esho k o st nc ,w c .F rin a e e ma e pe tt a i® r n n o e e sh c s, su h a t se t o t y x c h td e e tu f r se n o k c s ho o u put( .. a eg n o ilsh c ) t r str t s o o e nme tspe d g( ..aw ro o g t o l o k ,in e e a e rg v r n n in e g a rdr u h )w u d h v d e ing impa t o t g v r n a e i® r c s n he o e nme tbud e n t e e o e sh ul e ic g ta d h r f r o d l ita n a c d r a t n ba d o t so r e o he sh c . Fin ly t e c e ie t o u n e e c io se n he u c ft ok al , h o ±c n s f t e ¯ a l y r l w u d be f c io o h d e pa a t r o h mo l h sc lpoic u e o l un t n ft e e p r me e s ft e de,so t a h L u a c it u w ul no a y t t e poic e pe ime t r n u de h tt e c s r iq e o d t ppl o h l y x r ns u n r t is ¯ a u e lh u h w ilu r t t is o t h sc lr l .A t o g e l st a e h n heba o sis fasimpl icst nd r ist a ad mo e , it sh u d be st e d t a t e pr po d ide t c t n me h d l g is dl ol r sse h t h o se n i¯ a io t o oo y g n r le ug obea ie oa yg e a g - aema r e o o e e a no ht ppl dt n iv nl r e sc l c o c n micmo lw h de it o imisin g n s. pt ga e t Th epa riso g n da ol w pe r a ise sf lo s.InSe t n2,w c io edisc usst e dt cu hen e oin l de ¯ a l su e r e in ma r e o o sc lco r ul s c o c n mic mo e s, a pr se ta g n r lo l e o d l nd e n e e a utin f t e st nd r st a e y t d r e e ist g ¯ a ul s. In Se t n 3 w o e he h a a d r t g o e iv x in sc lr e c io e ® rt r t naef ra le n t espe i¯ a io a io l o nat r a iv c c t nint ef r o ne o e us ¯ a u e h o m fa nd g no sc lr l . W eilust a et ed r a io fsu har l l r t h e iv t no c u einSe t n4 o h c io nt eba o sis fast nd r a ad go t r w hmo l de.Fin ly al ,inSe t n 5 w isc ss t eimpl a io o he u e f r c io ed u h ic t ns ft ser l s o pr c ic lmo e l ga d poic n l sis a d pr se tc n l d gr ma k at a d lin n l ya ay n e n o cu in e r s. 2 F i c al l s ru esare n ed to fl l e m ac roeeed u l os yc c on i m od el om c s G o e nme u g tc nsta ,ta o y sh c s,a vr ntb d e o r int r nsit r o k ndt xsy e a st ms Ine a ishingt eba o cu st bl h sisf rin l dinga¯ a u einama r e o o sc lr l c o c n micmo e , dl o emu o k¯stt heg v r me tbu g tc n r in ,w ic a e t ef lo n stl o r ot o e n n d e o st a t h ht k s h ol w in a d r f r in d r t ime gst n a d o m isc e et : 3 Bt Bt ¡1 + ¿t= g + It t ¡1 Pt Pt () 1 P t w e e ¼t ´ P¡1 ¡1 is t e t { t in° a io r t . F r t e g v r me t t be hr h ime t n ae o h o en n o t sov n ,t ese o d t r o her h - n sid ft l e t h c n e m ft ig tha d eo hepr v u e pr ssio h s t e io s x e n a o bee u lt r .E® c iv l ,t isc nbec n e e san - o zi g mec n it n q a oze o e t ey h a o sid r da oP n a o d io , w ee h r byint imit it rt ea e t a eh l in hel ,e he h g n s r od gaze oa un fa t int r mo to sse s he a g e a e rt ea t e e enov l t n( h irpr eisze o .Ina yst nd r g r g t ,o h sse sr c iv aua io t e ic r) n a ad mo e it pt d lw ho imisin e gd bth l e s,t is is t et a sv r l yc n io t a h d od r h h r n e sait o dit na t c e t obo d h l ing t th s t n od s ha a obe v r e .T h r ma in e ms sa t a o he e i¯ d e e in gt r y h tf rt c r e tl v lo e obec nsist n it h ure tst t s o h c n my n u r n e e fd btt o e tw ht ec r n a u ft ee o o ,a y d v t n fo t x o e ia io r m a rspe ing pl n a n po tin t e f t e { d e t a y nd a s ta y in h u ur u o n sh c s a e t gr v n e o k ® c in e e u ,spe in ,in e e a e o ° a io { h s t nd g t r str t s rin t n a obe ba k d ce byc ng sint ein r n s a hedispo lo h o e n n .A n t e a f ha e h st ume t tt sa ft eg v r me t o h rw yo ga r spin h mein uit nc me f o sov gt ebu e o r in gt esa t io o s r m l in h dg tc nst a tba k a d cwrs in ( ) h g e t el v lo e lde o a s t e sum o stpr r e c s 1 :t is iv s h e e fr a btt d ya h fpa ima yd ¯ it pl s t el v lo e u h e e fd bta imeze o tt r .Ift c u l t n o e ia io s in pl n e hea c mu a io fd v t n and t x s fo pl n e e pe d u e is n tpr v n e t a n sy e t al , t a e r m a n d x n it r o e e t d oh ppe st ma ic ly he c r e t l v lo e u r n e e fd btmig t po e t ly in r a t a no d sir d l v lo v n h t n ial c e se o n- e e e e re e e pl d .T h f c x oe is a tpo t t he n e f rf r a d l o ingpl n in ,w r a t g in s ot e d o ow r o k a n g a r n in ar a t n t o k a t e c u ,in o d rt v id f t r n a ed btpa h e c io osh c s s h yo c r r e oa o u u eu st bl e t s. w e e B t st nd f rt { t n min ld bt t is r a ima y spe in ,¿t t x hr a s o ime o a e ,g e lpr r nd g a c le t n in r a e ms, a d It ´ 1 + it t e n mina t r st r t o bo d ol c io e lt r n h o lin e e a e n n s. Simpl pu ,t c n it n st t s t a h g v r n y t his o d io a e h tt e o e nme tha t s oissu de opa e btt y f r spe in in e c ss o t x c le t n Se nio a e r v n e is n ge t d f r o nd g xe f a ol c io . ig r g e e u e lce o simpl it . T h g r g t sc lv r bl s d ¯ da v ic y1 ea g e a e¯ a a ia e e ne bo ema fc ur yo o sebebr k n oe d w in ot e o n t h irsu a e o ie in ma r e o o bc t g r s c o c n micmo e s u d in pr c ic . d l se at e Sov l ingt is e u t n f r a d w v h t h q a io o w r eha et a , 1 1 0 0 1 i i X Y ¼t j 1 Y ¼t i 1 B t i 1 Bt + + A + + A + + @ = [¿t i 1 ¡g+ i 1 ] l @ + im ( 2) + + t + i 1 ! P t i 0 j 0 It j 1 It i 1 P t i 1 + + + + + + = = j 0 = St nd r a t e t o t in ¯ a l sur in l r e sc l ma r mo e s a a dpr c ic o b a sc lco e a g - ae c o d l T h ¯ a ul s u d in e ist gma r e o o e sc lr e se x in c o c n micmo e s,ba d o ma t indl se n in a in gbu e a ysov nc e u e dg t r l e yr q ir dby( ){ a de e t e yr l go tu a ede 1 n ® c iv l u in u nst bl bt pa h { no mal v l ea ust n nt er v n ts r lyin ov dj me to h e e uesid ft eg v r n eo h o e nme tbu dIn t is f a w r , t e mo e a y a t o it is a t e in t e se se o e pe 1 991 )in f ra it h r me o k h n tr uh r y c iv h n fL e r( soa s se s it c n r lv r bl s in e n e tyo a ol c io n e t s o t o a ia e d pe d n l ft xc le t na dd btissua c ,int ema n ritc n e s ne h ne o sid r mo ec n e ie t r o vn n. 1 4 g t2 In t is w y ec n w it n e e ict x sy e a e. h a ,w a r ea yg n r a st m s, ru ¿t= ¿ ( t t : )+ ¿t le c;y ;:: ( 3) w e e t e ¯stpa to h e u t n e hr h r r ft e q a io mbo s t e n r lt x sy e o he die h o ma a st m ft e o o ( c me t x s, c n mpt n t x s, e c) r pr se t g t e a t ma ic c n my in o a e o su io a e t ., e e n in h u o t st bil t n pr pe t s o a isa io o r ie fbu e s, w il t e se o d c mpo e tr pr se t t dg t h e h c n o n n e e n s he r v n e a j st n e e u d u me tby t g v r me tt g a a t e sov n y P oic r a t n he o e n n o u r n e l e c . l y e c io t pe ma e t sh c s t t e e o my w u d sho u in t e ¯st pa t o t o r nn o k o h c no ol w p h r r f he e u t n w il t a sit r sho k w ul be c t r d f r b t e se o d Fisc l q a io , h e r n o y cs o d aee o y h cn . a rue c mpo n ft t x sy e in ( { c n t k l o co e r l s { ba al t e ¿t l sur u e sic ly h ne to he a st m 3) a a e v r u f n t na o ms, in l ding se e a y s o a ia e n t o y l g e a io s u c io lf r cu v r lt pe fv r bl s, o nl a g d v l e o e t in st t a ia e au s fc r a a ev r bl s. T h ser l sf rmo e c n mie ppr x t h c ua e c io osh c sby e ue o d le o o sa o ima et ea t lr a t nt o k t e ¯ a ut r y e e t e e h sc la ho it .N v rh l ss,so e me mpir a v e esuppo t t e c pt r ic le id nc rs h a u in fa t a o e n n h v u it su h ar e e e ty o n( 998)h s go c u lg v r me tbe a io rw h c ul .R c n l ,B h 1 a pr v e e id nc h tg v r me t t k o r c iv o id d v e et a o e n n s a ec r e t eme su e inr spo a rs e nset isod t r n e t v r n u st bl re pl siv u ba c s oa e ta n a eo x o epa h f rde .B a d o t n l sis t o bt se n hea ay o imese ie d t o h nit d St t s,h nd e id nc h tt e g v r me t ft r s a af rt eU e a e e¯ s v e et a h o e n n h s h o ic ly r a t d t inc e se in t e de - o G D P r t by a j st g it a ist r al e c e o r a s h btt a io d u in s pr r ima ybaa e l nc . In pr c ic ,mo at e stmo e l r h v pt d f rabr a l d le s a eo e o o d ysimil rspe i¯ a io o a c ct n f t e ¯ a l su e r l .In mo a s,bud e a y a u me tis af n t n o he h sc lco r u e stc se g t r dj st n u c io ft d a c o v r bl suc a d ¯ ito e r m it t r e au in o d rt ist n e fa a ia e h s e c rd btfo s a g tv l e re o impo t e t a sv r l y c n io o g v r me td bt se h r n e sait o dit n n o e n n e .A t x d e e c r l a - i® r n e u e is u d in mo e s su h a M U L T IM O D ( F)a d N IG EM ( a io a e a c se dl c s IM n N t n lR se r h Inst ut ){ w e e h h n eint x t nisaf c io ft bj c iv a ia e it e h r byt ec a g a a io un t no heo e t ev r bl . A le na iv l ,so t r t e y memo e s spe if h irr e int r o e e s { f rin a c ,in dl c yt e ul s e ms fl v l o st n e M SG 2 ( amo e e e o dbyM c d ld v l pe Kibbina dSa hs){ w e e h a a eit l n c h r byt et xr t se f 3 is a u e in r f r nc ot eo e t e v r bl . T oilu r t ,at x di® r n e dj st d e e e et h bj c iv a ia e l st a e a - ee c r l o l beso u ew u d mev r n ft ef lo ingg ne icf r a ia to h ol w e r o m: ¡ ¢ ¡ ¢ ru ru ¤ ¤ ¿t le = ¿t le + a x¡1 ¡x¡1 + b x¡1 ¡x¡1 ¢ ( 4) t t ¡1 t t w e exist eo e t ev r bl i..g v r me td bto e c ) it na e isk hr h bj c iv a ia e( e o e n n e rd ¯ it ,w ha st r d no in hest a e t gt e dyst t au ,a a ev l e ndaa dbt espe do d u me tpa a t r n h e fa j st n r me e s, w ic a e c l a e .¢ ´1 ¡L st n s f rt e¯std e e c o r t r h h r aibr t d a d o h r i® r n e pe a o . T h u c io a o m a ef n t n lf r ndc l a io ft sc lco er l aibr t no he¯ a l sur u einamo e a d lc nbe o o sid r bl fc n e a eimpo t n einin u n in h ut to h tmo linsimu a io ra c ° e c gt eo pu ft a de lt n A n t bl e c pt n is t e Q u stmo e se by t e Eu o a Co o a e x e io h e d lu d h r pe n mmissio , in w ic ¯ a d n h h sc la j st n u me tin r spo se t e ia io s o e oit t r e a iot k s pl c o t e e pe d u e sid o e n od v t n fd btt s a g tr t a e a e n h x n it r e f t eg v r me tbu g t h o en n d e. 3 A r v w o x in ¯ a l su e r l s in ma r e o o e ie fe ist g sc lco r u e c o c n mic f r c st mo e s c n be f u in o e a ing d l a o nd P ¶e a d H ie r 20 0 1 ) e z n r be t( .A mo e d t il d a ay o h u d r n g o h se r l s is c n a e r e a e n l sis ft e n e pin in s ft e u e o t in d in M it h l ta. 20 0 0 )a d B r a ta d Z h n 1 996a . c e le l ( n yn n a g( ) 2 5 e e c s.F rin a e it h l ta. 20 0 0 )c mpa et e nseo a a dx r ise o st nc ,M c e le l ( o r her spo fst nd r ise v r n o h ¯ a ul s o IG EM ,M SG 2 a d M U L T IM O D .T h y sh w d e sio ft e sc lr e fN n e o ga r phic lyt a h al h tt eimpu ser spo sef c io oash c l e n un t nt o king v r me te pe io e n n x nd t r i® r id l ,r n in r m ar l t e ymo o o u ed e sw e y a g gf o e a iv l n t nica j st n oan n in a d u me tt ol er a j st n d u me tpa h r a ta t .B y n ndZ ha g( 996b)aso¯ d t a h e nseo a in 1 l n h tt er spo fv r a e c n d e u esu a t lyo t bl s a i® rq it bst n ial n heba o le n t est n r d ¯ a sis fat r a iv a da dise sc l r l s.T h y po to tt a h v l s o h f e ba k c e ie t in mo e a y ue e in u h tt e aue ft e e d c o ±c n s n tr a d ¯ a e d c u c io c n st o gy in u n e t e d na n sc lf e ba kf n t ns a r n l ° e c h y micbe a io ro h v u fa mo e ,so t d l me ime in u w n e o n a t d rimpl u e w y a sibl a s.Itis c n l d d o t e ba o cu e n h sis o h e id n et a e e al ,t r apa t u a l ft is v e c h tg n r ly he eis ric l ryimpr c e iseun e st n in f d r a d go h we o o s r spo t sc lpoic c io s.L a l ,B a r l ta. 1 994)aso o c n mie e nd o¯ a l ya t n sty r e le l ( l ¯ d t a he impl me t t n o he ¯ a l y r l h s a sig c n ® c n n h tt e n a io ft sc lpoic u e a ni¯ a te e to mo e o r ie inc mpa in h a ul s o IG EM ,M U L T IM O D a dM SG . d lpr pe t s o r gt et xr e fN n D e e t e v r t n in r suls,l te c n n s e ist o t pr pe o muspit h a ia io e t it l o se su x s n he o rf r l t n in t r o h dy a a io e ms ft e n mic a ust n o dj me tc mpo n ft e ¯ a ul s in t ne to h sc lr e he l e a u e e 4) it r t r ,i..( .Itis n tsu pr g se o t e w e sc pe o ssibil ie o r isin ,ba d n h id o fpo it s, ta h tin pr c ic , a w e v r t o at e id a ie y fspe i¯ a io is e id n o he f r l t n c c t ns v e tf rt o mu a io o sc lr l s in ma r e o o f¯ a u e c o c n micmo e s.A s n t d in M it h l ta. 20 0 0 ) h dl oe c e le l ( ,t is w idev r t f¯ a u e o n a ie yo sc lr l sf u dint el e a u eh h ig t hel c fa r e n h it r t r ig l h st a ko g e me t a n stmo e l r r g r in hea o ia ef n t n lf r f rt e u e mo g d le s e a d gt ppr pr t u c io a o m o h ser l s.A s a¯stin ,t ec l a io ft a i® r n er l s r q ir s t r put h aibr t no het xd e e c u e e u e heid n i¯ a io e t ct n o a g tv l s f rt e r l v n sc lv r bl ( su ly d ¯ ito e ) h is ft r e aue o h e e a t¯ a a ia e u al e c rd bt .T is r l t e yst a h f r a d iv nt el ngr e a iv l r ig to w r ,g e h o - unpr pe t s o hemo l h o r ie ft de .T emo e r d u te e n s t aibr t a e t e soc le sp e o d ust ntpa a t r i±c l l me t oc l a e r h - al d e d fa j me r me e s, w ic ,a c r in oM it he le l ( 0 0 ) ybeso w a f r lo d h c h h c o d gt c l ta. 20 ,ma me h tin o ma ra - o . So mo e l r h v pu su d mo e f r le e c s in t e de iv t n o h ir me d le s a e r e r o ma x r ise h r a io ft e ¯ a ul { se ,f re a e h d r a io ba d o a q a r t l ss f n t n sc lr e e o x mpl ,t e e iv t n se n u d a ic o u c io in B a r l ta.( 994) In a y c se w e d sig in t e r e a d c l a in r e le l 1 . n a , h n e n g h ul s n aibr t g t ek ypa a t r h sepa r d o o sid re pl ityw hed bth l e s h e r me e s,t e pe s on tc n e x ic l hot e od r a e in t emo e s t e r n l sin ,a d t nd t o u t est bil ya ay o r h d l h ya ea ay g n e of c s h a it n l sis n t e sy e f r d by t e bu g tc n r in ,( ) nd t e e u t n f r¿t le ,in h st m o me h d e o st a t 1 ,a h q a io o ru t e f r o,f re a e 4) h c l a io o h c e ie t a a d bin ( h o m f o x mpl ,( .T e aibr t n ft e o ±c n s n 4) is t e d n o t e ba o me a v c t d pr pe t s o h mo e l t n hn oe n h sis fso d o ae o r ie ft e d lsou io a d r spo se t sh c s, in ov g t e c n e a e use o u g me tin so n e n s o ok v l in h o sid r bl fj d e n me c se a s.A l h u ht is is apr c ic la dpa t lyv l ppr x t n tog h at a n r ial aida o ima io ,itd e n t os o g a a t e t tt r su t u r n e ha he e l ing¯ a u e is f ly c nsist n it t e pr pe t s o sc lr l ul o e tw h h o r ie f t emo e h d litis t y gt l se r in oco . T h t pe o a ko t r a o is y fl c fin e n lc nsist n y in mo lin ec de l gha be n c it ise by s e r ic d ma yf rit l c fmic oo n a io s st r in it u a ( 97 .A mo ef nd n o s a ko r f u d t n a t gw hL c s 1 6) r u a me t lc it ism o x g n u yimpo d¯ a u e n a r ic fe o e o sl se sc lr l sist e h irin e e tv n r bil y h r n ul e a it t h ot epo t r ise in s a dint eL uc s pa r s c ng s int e p pa a t r o he h a pe ,a ha e hed e r me e s ft mo e r pr se t gpr f r n e e h l g .)ma d l( e e n in e e e c s,t c noo y. . yno ir c l e dt td e tyl a oac a g hne in t ef r o aibr t n o h ¯ a ul . h o m rc l a io ft e sc lr e 6 3 A s trateg to i en f m od el as ¯s al y d ti y -b ed c c l u ru es os re l T h im o h r t g epr po ea ft est a e yw o seist e t ya¯ a l yr l se n ir l oid n if sc lpoic u eba de t e y o h o rie o h nt epr pe t s ft emo e th n .O nc h sc lco r u eis id n i¯ d d la a d et e¯ a l su er l et e, a dino d rt l eal r e sc l n r e osov a g - aemo e ,o d l nesh u dmo et n ft ±c n ol v oa yo hee ie t sou io l t nme h dsa a a eint it r t r ,l ef re a e h n s inJu l r t o v il bl hel e a u e ik o x mpl ,t eo e ila d e l 1 998) H ug s H al ta d M c d m ( 999) G a ra Jud ( 997 r ta.( , he le n A a 1 , spa nd d 1 )o M a imo a Sc t 1 999) r n nd o t( .In t f lo in he ol w gsubse t ns w br ° y r v wso c io e ie e ie me st n r e t nt est bil ya ay a da dr sulso h a it n l siso l e r a io a x c a io smo e s, f(in a )r t n le pe t t n dl t e o e dt e n u h npr c e opr se to rmo lba did n i¯ a io r t g n e ie de- se e t c t nst a e ya dr v wbr ° y ie o he t rmo e - se me h ds a a a e in t e l e a u e d lba d t o v il bl h it r t r . 3 1 Som e s d ard res l rom s i i . tan u tsf tab l tyan y i alsstheory A n iv n d n micst c st a io le pe t t n mo e a yg e y a o ha icr t na x c a io s d lc nbew it e ,w hr t n it o tl c fg n r l y t e f lo in u a ko e e ait ,in h ol w gimpl itf r ic o m, ut = F ( t ;";´t µ) u ¡1 t ; ( 5) w e e t e v c o t c n a s t e e o e o s a e o e o s v r bl s in t h r h e t ru o t in h nd g n u nd x g n u a ia e he mo e ,a e la h o d io a x c a io sint emo e ; he d l sw l st ec n it n le pe t t n h d l t yma ybed c n e isio v r bl s o h e o mica e t a ia e ft e c no g n s,su h a c nsu c s o mpt n o e lde io rr a bth l oding r s,o v r bl s o a e a f n t n o e isio a ia e bt in d s u c io s fd c ns,suc s r a t r str t s,o x g ha e lin e e a e re o e n u v r bl s l er n m sh c s o l yv r bl sd c dbyt eg v r me t o s a ia e ik a do o k rpoic a ia e e ide h oen n. T h v c o t c n a t in o a io s in t l w o e e t r" o t ins he n v t n he a s fmo io o h e o e o s t n ft e x g n u st t s,a d´tist ev c o fe pe t t n le r r t y ae n h e t ro x c a io a ro s,sa isf ingE t( t 1)= 0 ,w r ´+ he e t e o r t rE t( )d no e t e e pe t d v l e o he a g me tg e t e in o h pe a o ² e t s h x c e au ft r u n iv n h f r ma io ta a a eup t ime t t nse v il bl ot - .Fin ly h e t rµ c n a al ,t ev c o o t insalt est u t a l h r c ur l pa a t r o h r me e s ft emo e . dl In o d rt h h ig tt e ma c r c e ist s o he st bil y a ay o r e o ig l h h in ha a t r ic ft a it n l sis fa sy e su h a ( st m c s 5)a d t st e t a c t d in u io f r poic a ay n o r ss he sso ia e t it n o l y n l sis, t e a o e mo e a l e r d o -in a ise v r n o 5) a y d n mic h d pt d d lis in a ise /l g l e r d e sio f( .M n y a st c st a io a x c a io s mo l c n be a c r t l r pr se t d by t e o ha icr t n le pe t t n des a c u a ey e e n e h se t pe o ppr x t n N o w hst n g t y s fa o ima io s. t it a din his, t e d u n in t is Se t n h isc ssio h c io , a w l s t e poic s e la h l ydisc ussio e t a l t d o l beg n r l d v r a yt n x r poa e ,c u d e e aise e ye sil o h hl n n- in a ig y o l e rmo e s. dl W e be in by a ming t a t e mo e 5)h s a w l e n d st a y st t g ssu ht h d l( a e ld ¯ e ed ae sou io l t n.T h l e r d/l g l e r d v r n o he sy e a o nd t e de e e in a ise o - in a ise e sio ft st m r u h tr minist e dy st t a bee pr sse a icst a - a ec n x e d s, ¡ ut 1 = ¡ ut+ ª "+ 1 + ¦ ´t 1 0 + 1 t + ( 6) 7 w e e Á is t e a o ia e disc u t r t f r t is mo e . T a in a a bihr h ppr pr t o n ae o h dl k g n r t a y se finit lc n it n u0 a d simu a in t u r r to ia o d io s n l t gu singsoe y ( ,c n it n l l l 6) o d io a o sa e r aisa io s f r", w ln r ly l a t u a e t a e t r s f rut n mpl e l t n o t il o mal e d o nst bl r j c o ie o t a o l e e t al ioa et r n e sait o it ns g e by( ) o he h tw u d v n u lyv l t het a sv r l yc nd io iv n 7 .F rt t a sv r l y c n io s t r n e sait o dit n ohod e n e t d ase fst b it c nd io t l ,w e d oa d to a il y o it ns o t esy e ( . h st m 6) T h se st bil y c n it n a e d ¯ d by t e e e v c o s a c t d w h e a it o d io s r e ne h ig n e t r sso ia e it t eu a ee e v l e o h st m ( .W h n¡ is n n sin u a h a it h nst bl ig n au s ft esy e 6) e 0 o - g l rt est bil y a ay n l sisisba do h ig n au s o ¡1 ¡ .If¡ issin u a eh v oa ay se nt ee e v l e f¡ 1 g l rw a et n l se 0 0 t e g n r l d e e v l s o he pa ¡ ;¡ ) by me ns o, f re a e Z h e e aise ig n aue ft ir( 0 1 , a f o x mpl ,Q d c mpo io s ( eSims ( 0 0 ). eo sit n se 20 ) Inw a ol w n it o tl c fg ne ait n o h k fe po io , h tf lo s,a dw h u a ko e r l ya df rt esa eo x sit n w w la me t tt ma r ¡ ¡ c n be d c mpo d a P ¤ ¡1 ,w e e ¤ e il ssu ha he t ix ¡1 1 a eo se s P hr 0 is adia o lma r c n a in h e e v l e o ¡1¡ a d P ¡1 is t e ma r g na t ix o t in gt e ig n au s f¡ 1 n h t ix 0 o e te e v c o s. fl f ig n e t r A st t na y sout n t h mo e 6)r q ir s t a h t a io r l io ot e d l( e u e h tt e ime pa hs o a it fv r a e l o t e st bl ma if l o t e sou io spa e L e w ¡1 = P ¡1 ut bl s ie n h a e n od f h lt n c. t t ¡1 ¡1 a d »t = P ¡1 ¡ ( t+ ¦´t .L e s;t a d »s;t be t o po io s a c t d n ª² ) tw ¡1 n h se sit n sso ia e 0 w ht u a ee e v l e it he nst bl ig n au s.L e s d no e t r w o ¡1 a c t d w h tP e t s he o s fP sso ia e it t eu st bl ig n au s.T he au iq est t na ye u ibr m mu h n a ee e v l e n n u a io r q il iu stsa isf he t yt c n it n o d io , w = P sut= 0 ; 8 t s;t ( 8) pl s ase ft a sv r l yc n io u to r n e sait o dit ns, ¢ ¡ l im Á j t j = 0 u+ j 1 ! () 7 T h a v is e sy t e j e bo e a ose ustby sov g f r a d t e sy e in ( , sot a l in o w r h st m 6) ht w c n w it ( s w = ¤ w ¡1 + »s;t h r w h v o de e t sy e in e a r e 6)a s;t ,w e e e a e r r d he st m 2 s;t su h a w y t tt un a e e e v l e l in ¤ .Sov gf r a d t se f c a ha he st bl ig n au s ie l in o w r his to 2 e u t n y l s, q a io s ie d ¡1 ¡1 w ¡1 = ¤ w + ¤ »s;t s;t s;t 2 2 = j X ¡ ¢ ¡ ¡1¢ j ¡1 i ¤ Et w +j + Et ¤ »s;t i ¡1 s;t ¡1 ¡1 + 2 2 i 0 = g e t a h x c e v l fa yf ur r aisa io o h e o e us sh c s iv n h tt ee pe t d aueo n ut e e l t ns ft e x g no ok P 1 ¡ ¡1 ¢ i a de pe t t nse r r o dbeze o h nE t n x c a io r o sw ul r ,t e ¤ »s;t i = 0 ,a he ndt ¡1 + i 0 ¡ ¡1=¢ 2 j pr v us r l t n st t s t t s;t = l j 1 ¤ e io ea io a e ha ,w ¡1 im ! E t w + j .T h r h e ig t ¡1 s;t ¡1 2 h n sid o h a v e u t n is t e se ft a sv r l y c n io a t c e a d e ft e bo e q a io h to r n e sait o dit ns t a h d t h u st bl e e v l s. ot e n a e ig n aue 8 A co gc n it n l e ( r( l sin o d io ik 8)o 9)w ul be n e d t l e f rale pe t o d e de osov o l x c a t n le r r int io a ro s hemo e .A s d u dinSims ( 0 0 ) o h q il ium t dl isc sse 20 ,f rt ee u ibr obe u iq e yd t r e n c o d io o l n u l e e min do esu hc n it nsh u dbepr se tf re c x c a io a e n o a he pe t t n l e r rin t e mo e .T h st bl pa h o h a o ima e mo e c no c n ro h dl e a e t s ft e ppr x t d d le o my a be simu a e g e ( u l t d iv n 6)j stbya nd g( r( . ppe in 8)o 9) T h se fe ua io in ( e to q t ns 8)is u al d n t d a t e st b it c nd io o su ly e o e s h a il y o it ns f t esy e h st m.T h a it o dit n a u tt est bil yc n io s mo n oapa t u a in a o o -in a ) r ic l rl e r( rl g l e r c mbina io o he e do e us a e o e o s v r bl s in t e mo e .A l e n o t n ft n g no nd x g n u a ia e h d l tr a t e y by u iv l , sing ( n ( , o e c n w it t e st bil y c nd io a a l e r 6)a d 8) n a r e h a it o it ns s in a ( rl g l a )r l t n o o - ine r e a io ship be w e t e e pe t t n le r r a d t e st u t a t e n h x c a io a r o s n h r c ur l sh c s a e t gt ee o o , o k ® c in h c n my £ s ¡1 ¤ £ ¤ ¡1 P ¡ ¦ ´t= P s¡ ª " 8 ( 9) t t 0 0 3 2 Al ati w ays ofb u l i g m od el as ¯s al . tern ve id n -b ed c ru es l B a d o t e st bil ypr pe t s o h mo e d ra l sis,o se n h a it o rie ft e d lun e nay urid n i¯ a io e t ct n sc e h meisba do se ndi® r n e e tpie e le dya a a eint el e a u e c sar a v il bl h it r t r .Spe i¯ al , c c ly w il ebu dupo e sc min r m t nid a o gf o hesout n oR a ypr bl ms( sinCh r e l io st mse o e a ai t a. 1 994),a do h a a d impo io f\ poic ul s" s int el e a ur l( ) n nt est nd r sit no l yr e ,a h it r t e d aingw h d n mic o h st ,r t n le pe t t ns mo l el it y a ,st c a ic a io a x c a io de s. R a y t p sou io o h mo e mse - y e l t n ft e d l In o de oe d g n u y d r e t f r o t le ,o e sou io w u d be t r rt n o e o sl e iv he o m f¿ru n l t n o l o d r e a¯ a ul ba d e t e y o t d sig o he ma k t in t e mo l e iv sc lr e se n ir l n he e n ft res h de,in a f l- e g d o imisin r me o k e t ey c n e tw h t e mic o c n mic u l° d e pt gf a w r n ir l o sist n it h reo o ru f un a io s o h mo e . T h pr c d r w ul y l t c e ie t in ¿t le o d t n ft e dl is o e u e o d ie d he o ±c n s o imal n l ,a pt lya daso ndmo eimpo t n l ,t eo ima o m o ( t t :)in( r r a ty h pt lf r f¿ c ;y ;:: 3) f o a R a y se u A lho h t e st a e y pu su d in t e a v l e a ur rm mse t p. t ug h r t g r e h bo e it r t e w u d e t ilma y d sir bl c r c e ist s, t e u o c a \ R a y - y o l na n e a e ha a t r ic h se fsu h mse " t pe g v r me t is g n r ly l e t t a l sis o f iry simpl e e o mie oen n e e al imit d o he nay fa l i¯ d c no s. Su h ast a e yw u d bein e sibl o a g - aema r c r tg o l f a ef rl r e sc l c omo e s,g e t e e d l iv n hel v l o o e it o h e o o in t se mo e s a d t e e e fdisa g e a io . fc mpl x y ft e c n my he d l n h irl v lo g rg t n Se e a v r lpa r h h ig t t e c mpl x ie suro n pe s ig l h h o e it s r u ding t e sou io o R a y h l t n f mse pr bl ms, su h a Ch r a d Ke o ( 999)a Cha i e l 1 994) Sov a o e c s ai n he 1 nd r ta.( . l ing d n mico imisa io mo e ya pt t n d lin w ic t e g v r n h h h o e nme tma imise a e t t it x s g n s'u il y su e t t al Eu e c nd io s in a e t bj c o l l r o it n g n s'pr bl ms w u d be c mbe so , if o e ol u r me n t impo o ssibl , w h t e l v l o d g r g t n in l r e sc l ma r e o o e it h e e f isa g e a io a g - ae c o c n mic f r c st gmo e s. o e a in dl 9 St nd r impl me a io o \ p l y r e w e sov a ad e nt t n f oic ul s" h n l ing r t na e p c a io a io l x e t t ns mo e s dl N o mal a st bl sou io t a dy a , st c a ic r t n le pe t t n r ly a e lt n o n mic o h st , a io a x c a io s mo e ik t e o e pr se t d in Co l y a d P r sc t 1 995)o a imo a d d ll e h n s e n e oe n e o t( rM r n n Sc t 1 999) a e t ef r o o t( ,t k s h o m fasa dl - t q il iu d e pa he u ibr m.T h d l - t q iesa d e pa he u l iu is se e t dbypin in ibr m lce n gdo nt est bil yc nd io s a t c e ou st bl w h a it o it n t a h dt n a e e e v l s, o ig n aue rimpo d by me ns o ppr pr t ¯ a o dit n a in Ju l r se a fa o ia e n lc n io s s lia d e .a. 1 998) t l( . So meo hec n io ft o dit nsin( 8)ma a eace rin e pr t t nint r yh v l a t r e a io e mso l y fpoic r l s,a h sec n io ea epoic a ia e ( st ume t oe do e o sa d u e st e o dit nsr l t l yv r bl s in r n s)t n g n u n e o e o s v r bl s in t emo e .T h w y h st bil ya ay o hesy e x g n u a ia e h dl is a ,t e a it n l sis ft st m a a dw u dl a st h e u e l singc n it n it uth v gt e r th n o l e du ot er q ir dco o d io s,w ho a in or so t t h t pe o d it n l¯ a l y r e a o a e f rt e ¯ a u e in t ot e y fa d io a sc lpoic ul s dv c t d o h sc lr l he ma r - d lin it r t r . c o mo e l gl e a u e L e ' t yt r sp so ts r og a mein uit no h u c io t io nt ef n t ningo his poic ul s.Co ft l yr e nside ra st n a d ne ca a r w h mo e it a e t ma imising t ird adr o l ssic lg o t d lw h g n s x he isc u t du il yd r e r m c n mpt n ndw hd bt o n e t it e iv df o o su io ,a it e ,inw ic h r n e h ht et a sv r sait o it n a c t d w h d btt k s t o m, l yc nd io sso ia e it e a e hef r ¸ · + t jB t j + =0 l Et Á im j 1 ! Pt j + w e eÁ is t ed o n a t r sin hest n a da l sis o tin da v o l hr h isc u tf c o .U gt a d r nay u l e bo ew u d impl t a o h t a sv r l y c nd io t y h tf rt is r n e sait o it n ohod n e u t n o he t pe o l ,o e q a io ft y f ( 8)sho dbea de ot ul d dt hesy e o r r e o it n a dc n r in s.T h st m f¯sto d rc nd io s n o st a t is c n it n w u d t k t f r o l a / o - in a o o d io o l a e he o m fa ine r n n l e rc mbina io o e lde t n fr a bt w h o he a ia e in t e e o o , suc a c n mpt n, ( t rt e c pit l it t rv r bl s h c n my h s o su io c)o h a a st c k) o k( t , ¶ µ Bt ;c;E t[fd ebt c+ 1 ;k+ 1 :: ] : ;sh c st = 0 (t ok f n t n ebt u c io d t t : ) ;: : Pt a d sh u d hod in e c sin l pe io o ime h c n it n w ul be u iq e n ol l a h ge r d ft .T is o d io o d n u, a d w u d r pl c h r n e sait o d io in t ese fo imait o it n n o l e a et et a v r l yc n it n h to pt l yc nd io s u d t l e f ralt ev r bl s in t emo e .O new yt iv mee o o se osov o l h a ia e h dl a og eso c n mic in e pr t t n t h t pe o o dit n w u d be a f lo s.O nc a e t in e t r e a io ot is y fc n io o l s ol w e g n s tr n l t tt g v r me tc mmit it l obe sov n ,t e be a e in su h a aise ha he o e n n o s se ft le t h y h v c w yt a de dt er su t ge u ibr a h tin e h e lin q il ium is st t n r n h o e n n bt a io a ya dt eg v r me tde is v l d a d h l byt e a e t aue n e d h g n s. Fo a eo o r m n c n mic po t o v w a d f r t e pur se o poic a ay in f ie , n o h po s f l y n l sis, t e in u io be in t e f r l t n in ( h t it n h d h o mu a io 8)mig tbe c n e e a bito u e h o sid r d bsc r . A lho h impo g su h c n it n t sov f r t v r bl s in t mo e is t ug sin c o d io s o l e o he a ia e he dl t c n al o r c ,itis so w a e h ic lyc re t me h tmo ed u tt iv mee o o r i±c l og eso c n micme n g a in in t e f a w r ft e mo e in nay d h r me o ko h d lbe ga l se .Spe i¯ al ,w n impo gt c c ly he sin he 10 t a sv r l y c n io f rbo ds,o e ma w n e h h in r n h g v r n e sait o dit ns o n n y o d rw ic st ume tt e o en n o l r me tw u dbemo ingo h v n f o st n e v nt ee e to,f rin a c ,ar c ssio .T heimpl it ee n ic f r l t n in ( e e t h wa e t in e n l h o o mu a io 8)r ° c s o g n s t r aiset ec mmit n r m t epa t me tf o h r o heg v r me tt ft o e n n obesov n .W he h o le t nt isc mmit n me tisin e n l d,sov nc t r aise le y is a t ma ic u o t .In e d a w y t r w it t e st bil y c n io f rbo s w u d de, a o e r e h a it o dit n o nd o l be , ¶ µ Bt ¡1 ;c ;;:: o k t E t[fd e bt c+ 1 ;k+ 1 :: ] f c io d ebt (t t : ;sh c s t : ) = un t n Pt sot a h timpo gsov n yimpl sac r a o m t l ef ra e t beie s.T h sin l e c ie e t inf r osov o g n s' l f is is w y f rt e sou io t be u ue t e e sh u d be o su h a c nd io pe h o h lt n o niq hr ol ne c o it n r e pe t t n e r r x c a io in t emo e . x c a io r o /e pe t t n h dl T h impl ite d g n u ¯ a l y r l r l s o a a mpt n t tg v e ic n o e o s sc lpoic u e e ie n n ssu io ha o e n n s a e c e ibe t u g n r t g t o c me t a g n s in e naise t r me t r rd l , h s e e a in he ut o h ta e t t r l he r l o e e y his f r o h r l ,h w v r ® r fo t e dr w c h t u ec mpl t l .T o m ft e u e o e e ,su e s r m h a ba kt a t is a mpt n o r d it is ma t in d d spit al c fsy e t h ssu io fc e ibil y in a e e e a ko st ma icst bil a isa io o t e pa to heg v r me tin r spo set t n n h r ft o e n n e n oimbaa c s in t c no . ln e hee o my T h r ar pu a io pr bl m. e eis e t t n o e 3 3 B u l i gf as . i d n orec t-error-b as ¯s alru es ed c l Fo te¯ a r m h sc lpoic po t o ie w w u d be in e e e in k o in w a l y in fv w e o l t r st d nw g ht ru a u to e e u iv nby¿t le w u dst bil mo n fr v n eg e o l a ised bta dma et et a e sait e n k h r nsv r l y c n it n h l .T he a o c a v c t d in t is pa ris a e t nsw rt h o d io od ppr a h d o a e h pe bl oa e ot is q e io u st n,w il tt e sa t h ea h me imeis f ly ba d o t ese fc n io in ( . ul se n h to o dit ns 8) T h g v r me tbu g tc n r in 1 )is a u st bl d e e c e u t n in e oen n d e o st a t( n n a e i® r n e q a io ra e e ld btin f ra ¿t¡g is st t n r n It is g e t rt a o e s sh w soa s a io a ya d ¡1 r a e h n n .A on t inM it h l ta. 20 0 0 ) h a da dpr c ic o c e le l ( ,t est n r a t ef rbuil in x g n u ¯ a u e d ge o e o s sc lr l s t ie ospe if r st c yag e l me to t{ w tw al¿t le { a u c io fpa iv ne e n f¿ ha ec l ru saf n t no stde bt sot a h r sulingc e ie ta t c e t h tt e e t o ±c n t a h d opa e std btw e sov gf rt e t o h n l in o h w e u t n h ppe s t q a io s a n obe l w rt a o e h t oe u t n a l sis is h l u o e h n n .T is w q a io s nay e pf l be a se it c n r in t po cu o st a s he ssibl v l e o t e c e ie t in t ¯ a r l . e au s f h o ±c n s he sc l u e N o e h l ss,t eq st na utt espe i¯ a io ft er l se fr ma s o n n t ee h ue io bo h c c t no h u eit l e in pe , a d in a d io , in mo e s n td a in pa a it o h g v r n o k n d it n d l o ispl y gse r bil y ft e o e nme tbl c t et oe u t n a ay w ul o h w q a io s n l sis o dn tbev l aid.T h t oe u t n r a n gw l is w q a io s e so in il be h l u o s. e pf lf ru Fo t r m hese fst bil yc n it n to a it o d io sin( ec nd ¯ et 8)w a e n hest bil yc nd io s a it o it n a c t d t h a ev r bl e sso ia e ot est t a ia ed bta f lo s. s ol w ut t st t v r bl d bt in a g e mo e , in w ic t g v r me t h s t he a e a ia e e iv n dl h h he o e n n a o f l lit pe io - - r d bu e o st a t e ' a met a h r o yo u ¯ s r d by pe io dg tc n r in .L ts ssu h tt e eis nl ne b g v r me ta tint ee o my e s;tbet l me to s;tr l t dt e , o e n n sse h c no .L tw hee e n fw ea e od bt De¯n on T he st b it c nd io a t c e t d b . L e ' deno e by b ½ i ti : a il y o it n ta h d o e t ts t t 11 a d l tP s;b ½P s bet e c r e n in o fP s.T h r n e sait o it n n e h o r spo d gr wo et a sv r l yc nd io a c tdt h o e n n e sso ia e ot eg v r me td bth s ac r e nd a o r spo ingst bil yc n it n g e a it o d io iv n by wb = P s;but= 0 ; s;t (0 ) 1 T oc mpu et isst bil yc n it nw e e ope f r t o t h a it o d io ene d dt ro m hest bil ya ay a it n l sis o he sy e ( . T h e u ibr m w se e tby sov g j in l ( n ( ft st m 6) e q il iu e lc l in o ty 6)a d 8)is o e in w ic t e g v r me t is c e ibl , a d a a c n q n e a e t a j st n h h h oen n rd e n s o se ue c g n s d u te h irde isio s sot tg v r me td btis v l d a d t e r sto r nsv r l y c n ha o e n n e aue n h e ft a e sait c n it n h l e e w e t e poic r a t n t sh c s is no - x in , i.. o d io s od, v n h n h l y e c io o o k n e ist g e ru ¿t le = 0 .In o d rt l e t e ind t r a y pr bl m t a r e osov h e e min c o e h tmig ta ise in c se h r a t e a e t w r n tc e ibl c n e in h c mmit n r m t e pa to he h g n s e e o r d y o sid r gt e o me tf o h r ft g v r me t e n e t ssig c n e tt n e e t a l yr a t n t le . o e n n ,w e d oa n o t n oa v n u lpoic e c io ,¿ru T od h ot is,w l ef r¿t u gt est bil yc n it n ( 0 ) n t eg v r esov o sin h a it o d io 1 ,a d h o e nme tbu e o st a t( ) n dg tc n r in 1 ,sot tw e ha eg t ¿t = fun t n vt t ) c io ( ;u ¡1 w e e vt is a v c o o t in gt e sa e e n s a ut w h t e c pt n hr e t rc n a in h me l me t s it he x e io o t h n using t e g n r lspe i¯ a io o h ¯ a u e ( o e h rw h fb.T e , h e ea c c t n ft e sc lr l 3)t g t e it t e pr v us e ua io h e io q t n,w a e pr ss ¿t le a af c io o h v r bl s in t ec n x e ru s un t n ft e a ia e he in o ma io se , fr t n t ru ¿t le = fun t n ( t t ) c io 0 v ;u ¡1 (1) 1 O nc w h v id n i¯ d a f n t na o m f rt e g v r n e c io , w e e ae e t e u c io lf r o h o e nme tr a t n e c n sov t g tt e e u ibr m v l e o l h v r bl s in t e e o o by a l e o e h q il iu au s falt e a ia e h c n my me n o: as f ²T h r d c d f r o h a u e( 1 ) e e u e o m ft et xr l 1 . ²T h l e r d sy e ( . e in a ise st m 6) ²T h se fst bil yc nd io P sut= 0 ;8 min P s;but= 0 e to a it o it ns t us W ec n a r n et is se fe u t n a d w it a ra g h to q a io s n r e · ¸ ¡ 0¢ ut 1 ¡1 0 + = ¡ ¡ ut+ ª0 "+ 1 t 0 1 ´t 1 + ( 2) 1 w e e t e ma r e ¡ a d ¡ a e a o ia e y r o g nise ma r e o 0 , hr h t ic s 0 n 0 r ppr pr t l e r a d t ic s f¡ 0 1 ¡ ,¦,P s a dt el e rf nc io n h in a u t nin( 1 ) ua io 1 2)sho st est bl l t n 1 .Eq t n( w h a esou io 1 o u fo rmo e o l hev r bl s in t e mo e ,ut d lf ralt a ia e h d l .Ev r a ia e is sov d a a e yv r bl le s f n t no stv l e ft est t n o t o a ia e n h o k ® c in u c io fpa au so h a ea dc n r lv r bl s,a dt esh c sa e t g t e e o my l e n t ey e c n sov f re c v r bl in t e v c o t a a h c no .A t r a iv l ,w a l e o a h a ia e h e t ru s f n t n o a g d e d g n u st t v r bl s a d e o e us st t v r bl s.In u c io fl g e n o e o s a e a ia e n x g no a e a ia e pa t u a ,o rv r bl fin e e t le w u d besov d a f lo s, ric l r u a ia eo t r st¿ru o l l e s ol w ru ¿t le = fun t n e o e us st t st ;e o e o s st t st c io ( nd g no a e ¡1 x g n u a e ) ( 3) 1 12 w e et ec e ie t h r h o ±c n sint el e rf n t n( 3)a ee pl itf c io s o h e p h in a u c io 1 r x ic un t n ft ed e pa a t r o h r me e s ft emo e ,a dw u de e t al h n ew e h yc a g .W h n d l n o l v n u lyc a g h nt e h n e e c mpa e t a da d r l s,t e r l o r d ost n r u e h u ein ( 3)sha e t e simpl it n e o o 1 rs h ic ya d c n mic in u io o h se r e w il a he sa t t it n ft o ul s, h e tt me ime a o t e L u a Cr iq e a d v ids h c s it u n f e s f o j g me tt r e r m ud e n hese e t n o h spe i¯ u c io lf r l c io ft e c cf n t na o m. End g no s r e b se n t e r l t n b t e n e p c a io e r r a o e u ul a do h e a io e w e x e t t ns r o s ndsh c s ok Itsh u dbe¯stn t dt a h o it nincu in e ft y ol r o e h tt ec nd io l d gd bto het peo tin d ul e in ( a a c u t r r 8)h s o n e pa tin t e f r a io g e by ( ,in ov , in t r o h o mul t n iv n 9) v l ing e ms f t e a v - isc sse e a e it e l a rn n- in a e a io sh be w e h bo e d u d x mpl ,e h ra ine ro o l e rr l t n ip t e n t e e pe t t n le r ra c t d w h a e t h x c a io a r o sso ia e it g n s'in e e a e f r c st »t ½ ´t t r str t o e a s, I , a d t e st u t r lsh c s.T of lo hee a e n h r cu a o k ol wt x mpl ,byc n r t n o st uc io I »t ´fd e bt c ;k: : ( t t:)¡E t [fd e bt c ;k:: ] ( t t: ) ¡1 w c n t e po ul t t a h g v r me tsh u d r ise o e r a r v n in e a h n st a e h tt e o e n n o l a rd c e se e e ue l e w h a e t e e a te pe t t n le r r in it g n s'r l v n x c a io a ro ru ¿t le = ¡ »I »t °b I w h ° me su in t e st e t o he g v r n e c io . T he e o o it a r g h r ng h ft o e nme tr a t n c n mic int it n be d t is id n i¯ a io h po h sis is r l t e y st a h f r a d. A s u io hin h e t ct n y te ea iv l r ig to w r in ial h r nod e tl kbe w e t le a d t ev r bl s r l t d byt ese it lyt e eis ir c in t e n¿ru n h a ia e e a e h t o a it c nd io ( , itsh u d be no e t tt e c e ie t° c n tbe fst bil y o it ns 9) ol t d ha h o ±c n a no u iq e y de e min d h ma k ad e e c w h r spe tt h id n i¯ a io n ul t r e .T is rs i® r n e it e c ot e e t c t n sc e pr se t d in t e pr v u su c io N e e t e e o c n id n if ° h me e n e h e io s bse t n. v rh l ss, ne a ety byr pl a ingt epr pe t s o h l io o a e f o ( 2){ in ase set is e ic t h o rie ft esout n bt in d r m 1 n h w u d ma eu ueit id n i¯ a io . ol k niq s e t ct n Co mbin g t c e ie tid n i¯ d by t e me n o l e a v w h t in he o ±c n e t e h a s utin d bo e it he impl d r l t n be w e »t a t e st uc u a no a io f o ( ,w u d g e ie e a io t e n I nd h r t r lin v t ns r m 9) o l iv u ar l t nsh o hef r s e a io ip ft o m ru b ¿t le = ° "" t t a c n be id n i¯ d a t e ¯ a ht a e t e s h sc lpoic co r r l . T a in t mo e 6) l y l su e u e k g he d l( a da n gt is r l o l o uc a eo t o s f lyc nsist n it he n ppe din h u ew u dpr d est bl u c me u l o e tw ht mo e n ra l sis, w r alo h be v ur le e n s t tt e l e a ur d lu de nay he e l ft e ha io a l me t ha h it r t e o ¯ a l su e no mal impo s o t e ¯ a ul w ul be t a sf r e ba k n sc lco r s r ly se n h sc lr e o d r n e rd c t h pr pe t s o h mo e se f ot e o r ie ft e d lit l. T h s,w r in it t e a ao o s spe i¯ a io s in ( n ( u o k gw h h n l g u c ct n 8)a d 9)w c n bu d e a il a ag r h t o n l o it m oc mput a e pl it¯ a u e e n x ic sc lr l .In summa y h st ps t ol w r ,t e e of lo f rt e c n r t n o u ew ul be o h o st uc io fr l o d : ²St p 1 :P e f r t e st bil y a ay o he sy e ( ode e min t e ro m h a it n l sis ft st m 6)t t r e he st b it e s o h st m,a a il yne d ft esy e ssumin t le = 0 . g¿ru 13 ²St p 2:Id n if h x c a io ro e e a tf rde e e t yt ee pe t t ne r rr l v n o btst bil y r m t a it ,fo he r l v n o ( f( ,a dt e set o r spo d gr w s)in( og ss e e a tr w s)o 8) n h nu hec re n in o ( 9)t ue a¯stt n a iv e a io r e t t er l t nbe w e t le a h e e a te pe t t ne r rs) t e n¿ru ndt er l v n x c a io r o ( ( iaise o x mpl ,t n ) init l ,f re a e oo e . ²St p 3:D e e min t e v l o h c e ie t s)o h tr l t n o t e t r e h aue ft e o ±c n ( ft a e a io n he ba o t e st bil y a l sis o t e sy e a c mput t e st bil y sis f h a it nay f h st m, nd o e h a it c n io o h sy e o dit ns ft e st m. ²St p 4:Caibr t t e c e ie t s) h n c mpu e t e ¯ a l sur r l e l a e h o ±c n ( .T e o t h sc lco e u e byusin h c l a e c e ie ta d t e r l v n o it n f o ( . gt e aibr t d o ±c n n h e e a tc nd io r m 9) T h r l t n be w e t t opr se t d id n i¯ a io s sc e s,ba d o a e e a io s t e n he w e n e e t c t n h me se n l e r l g l a ppr x t nt heo ig a in a /o - ine ra o ima io ot r in lmo la esk t he u de r e c do tinFig e1 ur in t eA ppe ix h nd . Ex e t nsio n:Fisc lr l s f rno l a a ue o n-ine rmo e s dl T h d sc ibe ag r h ba d o al e ra o ima io c n asobe e sil e e r d l o it m se n in a ppr x t n a l a y a ie t l eh h yn n l e rmo e s,w h u a in or so tt h in a ppl d osov ig l o - in a d l it o th v gt e r ot el e r sou io o hemo e th n buta a in e me ia ein r me t l t n ft d la a d s n t r d t st u n . Th e eid ais t opa a t r h a ia e¿t le a af c io o r me e iset ev r bl ru s un t n fasu ie tse ±c n t o he v r bl s in t e in o ma io se ,ma u ba al o a g d e o e o s ft a ia e h fr t n t de p sic ly fl g e nd g n u st t a ia e a dc n e a ev r bl s n o t mpo a o s e o e usst t a ia e r ne u x g no a ev r bl s.T hepa a t r r me e isa io o l t nw u dbeimpl me t dbyme n o n e ibl u c io ik e ne a s fa y° x ef n t nl eapoy o l l n mia ( e o e a à ( )) re e a l e rf n t n,d pe ingo t pe c iv d c md n t d s ²),o v n in a u c io e nd n he r e e o pl x yo hemo e n t ev r c t n o her t na x c a io s h po h sis e it ft d la d h e i¯ a io ft a io le pe t t n y t e f rt e sou io 4 .In mo e f r lt r o ec ul w it , o h lt n r o ma e ms n o d r e ru ¿t le = à ( n o e o s st t st ;e o e o s st t st a e d g n u a e ¡1 x g n u a e ; ) ( 4) 1 T h to r me e saa hee a tf n t na o m f rà c u dt nber ¯ e ese fpa a t r ndt x c u c io lf r o o l he e nd u t h x c a io s e r r a eaw it o ,a itsh u dbet ec sea c r in n ilt ee pe t t n ro s r h en ise s ol h a c od g t he r t n le pe t t n h po h sis.T h r ¯ e n ft e sout n c n be ot a io a x c a io s y t e e e n me to h l io a ma deu g o x mpl ,t ed nH a na sin ,f re a e h e a ndM a c t( 994)t st hec mpu a io re 1 e .T o tt n o it bl it lv l e f rt ev c o fsu a ein ia au s o h e t rac u dbema ol deo h nt eba o hel e r sis ft in a sou io t h mo e . l t n ot e d l Ima ine w ha e t e st nd r ne ca a r w h mo e it c pit l( t g e v h a a d o l ssic lg o t d lw h a a k) a dd bt( t eh v e isc ssin bo e n w o k { o et e hn l g n e b)w a ebe nd u ga v ,a dt osh c s n ot c oo y (t n o et z )a d n opubl icspe d g( t .F re a e o mig tst r it ag ss n in g) o x mpl ne h a tw h ue rue o h o m, l ft ef r f r¿t o a a1 a2 ru ¿t le = a b¡1k¡1 za 3g 4 0 t t t t 4 ( 5) 1 O n mig tt in t it e yo h sou io in t r o,f re a e h e h h kin u iv l ft is l t n e ms f o x mpl ,t epa a t r d e pe t r me e ise x c a t n a o c fM a c ta io s ppr a ho r e ndL o e zo i ( 999) rn n 1 . 14 g e so in ia o dit n f rt pa a t r a ,a ,a ,a ,a d a .T h n if iv n me it lc n io s o he r me e s 0 1 2 3 n 4 e , by c nst u t n, t e pe t t n e r ra c t d t t e st bil y c nd io f r o r c io he x c a io r o sso ia e o h a it o it n o d btis e b »t ´fd ebt c;k:: ( t t:)¡E t [fd ebt c ;k:: ] ( t t:) ¡1 t e w c n r ¯ e t e a o ima io in ( 5)u t h e pe t t n e r r»t is a h n e a e n h ppr x t n 1 n ilt e x c a io ro b w it n ise a c r in ot h e o c o d gt hed n H a n a d M a c t( 990 )t st e a n re 1 e . T osu u m p,st p byst p,o e e ursou io ag r hm w u d bet ef lo ing l t n l o it ol h ol w : ²P o u a e a in ia u t n lf r f rt ppr x t gf nc io , st l t n it lf nc io a o m o hea o ima in u t n a1 a2 a ru ¿t le = a b¡1 k¡1 za 3g 4 0 t t t t ²Co mpu ein ia o it n f ra - a : t it lc nd io s o 0 4 { Co mpu eal e r l g l e ra o ima io ot t in a /o - in a ppr x t nt hemo e th n d la a d.O bl i rue ,a in ( 3) alit¿rue;l n ear . l t in t ee pl itsou io f r¿t a h x ic lt n o s 1 ,c l t { Co mpu e init lc n io f rt e pa a t r a - a f o t e l e r t ia o dit ns o h r me e s 0 4 r m h in a sou io t h l t n ot emo e ,byr n dl u ningt e n n l a e r ssio h o - ine rr g e n ru ne a4 a2 a1 3 ¿t le;li ar = a b¡1;li k¡1;li ear za;li g;li ear 0 t t near t n n near t ²Co mpu et ee pe t t n e r r t h x c a io ro b »t ´fd e bt c ;k: : ( t t:)¡E t [fd ebt c ;k:: ] ( t t: ) ¡1 ²Ch c he h rt ee pe t t n e r ris w it o e kw t e h x c a io r o h en iseo o . rn t ²Ift ea sw ris n ,r pe tt ee ima io o e u ef rt en wse ft h n e o e a h st t npr c d r o h e to ime se ie n it r t u t he r su t r s,a d e a e n ilt e l inge pe t t ns e r rc n be c n e e x c a io r o a o sid r d aw it n ise h e o . F lo in h sest ps,w il n ol w gt e e ew le dup w ha¯ a l yr l h tisc nsist n it sc lpoic u et a o et w h t e pr pe t s o h mo e , a d w ic c e ie t a e d pe d n n t it h o r ie ft e d l n h h o ±c n s r e n e to he d e pa a t r o h e p r me e s ft emo e . dl 4 A b asc m od el i In t is Se t n w impl me tt e id a o t ba o st nd r o imisin h c io e e n h se e s n he sis fa a a d pt g bu e c cemo e .T h sin ss y l dl emo e u l e d lo tin dbe o l wis av r n ft est nd r o a ia to h a a dne ca a r w hmo e ,in ov gpr d c io n a io sst c a icd ur n e l ssic lg o t d l v l in o u t na dv r u o h st ist ba c s. T h mo e use t l st a eo rid n i¯ a io sc e . is d lis d oilu r t u e t c t n h me 15 4. 1 Des ri onof c pti the m od el T h e o my c n s o c n in u o e t a, in n ey l e h u hod e c no o sist fa o t u m fid n ic l ¯ it l iv d o se l s, a d bo h mo e a y a ¯ a ut o it s. T he t pic lh u h l ' pr f r n e n t n t r nd sc la h r ie y a o se od s e e e c s o e h sin l o su v rt e gec n mpt n c mmo it io o d yin t ee o o h c n mya eg e by r iv n , E0 1 X ¯ tl g( t o c) ( 6) 1 t0 = w e ec d n t s c n h r t e o e o sumpt nbe w e ta io t e n ndt+ 1 .T h e e n a iv g n er pr se t t ea e t u s it a c mu a e c pit lst c ,k¡1 ,t o uc ure to t to t eba se s c u l t d a a o k t opr d ec r n u pu n h sis ® o fast c a icCo D o ga t c n l g t= z k¡1 ,w e ez d n t s ar n o o h st bb- u l s e h oo yy h r t e oe adm tt c mpo e t t t c n l g . P t is t e pr e l v l Ea h h u h l c o s t o n n o e h oo y h ic e e . c o se od ho se he se u nc s c , k, a d d bth l in s, B t g e t e l v lo ic s, t e n min l qe e t t n e od g , iv n h e e fpr e h o a in e e r t , It a d t e r aisa io o t e o e o s sh c s t a ma imise t r st a e , n h e l t n f he x g n u ok h t x s ( 6) 1 ,subj c oit r so r e c n r in , e tt s e u c o st a t c+ k+ t t Bt Bt ¡1 = yt+ ( ¡±) t + It 1 k¡1 ¡¿t Pt Pt (7 1 ) T h g v r me tissu s o e pe io - t r y d bt a c le t t x s, ¿t t e oen n e n - r d ma u it e , nd ol c s a e , o pa o n e o e us se ue c fpubl x n it r ,g,a d t yf ra x g no q n eo ice pe d u e t n hebu d n o st r e fpa d bt e ,issu d in t¡1 , e It t B ¡1 Bt + ¿t= g + t Pt Pt ( 8) 1 T h r nd m e v o e a o n ir nme t in t e e o o n h c n my is c pt r d by t r e e o e o s a ue he x gn u sh c s:²z t,w h is ash c t e hn l g ( t ;²gt,d n t gash c t ok hic o k ot c oo y z ) e o in o k opu ic bl spe d g t n ²I t,st n in o sh c t o a t r str t s, It e hn in ,g;a d a d gf ra o k on min lin e e a e .T c n l g a d pu ic spe ding a e a oo y n bl n r ssume t c a g in a c r nc w h t e d o hne c o da e it h ir r spe t e sho k a d e h e c iv c s, n x ibitso d g e o r e c ( a r d by ½z a d me e r e fpe sist n e me su e n ½g )a o n ak w me n g e byz a d g ,r spe t e y r u d no n a iv n c iv l ,sot a , ht ss n ss e z = ( ¡½z ) ss + ½z z ¡1 + ²z t 1 z t t g = ( ¡½g ) ss + ½g g¡1 + ²gt 1 g t t ( 9) 1 ( ) 20 G iv n t e f c s o his pa ro ¯ a e h o u ft pe n sc lissu s,t e mo e a y a t r y is a e h n t r u ho it ssu d t ol wasimpl ul fma t in gt en min lin e e a ec n a t me of lo er eo in a in h o a t r str t o st n , k e gin a io r un s t r e .W ew la met a hemo e a ya t o it e pin ° t na o dit a g t il ssu h tt n tr uh r y c nrl t o t os hein e e a e impe f c l ,sot a , t r str t re ty ht It= Iss + ²I t ( ) 21 W it o tl c o e e ait ,t t x sy e in t is e o o w lbe a me h u a k fg n r l y he a st m h c n my il ssu d t obe c mpo d o me ¯ e a u to e e ue g e by ¿0 .In a d io , t o se fso x d mo n fr v n iv n d it n he 16 ¯ a u h r yw lbea me oc le tal mpsc la t o it il ssu dt ol c u sum t xe r r e ost bil a a ma k dt a ise rue l d bt t sot tt xc le t n a a h pe io o imew u d bee u lt e ,¿ ha a ol c io te c r d ft ol qa o ru ¿t= ¿0 + ¿t le ( 22) w e e ¿t le w lbema ee u lt h r ru il d qa o ru ¿t le = ¿b ( t ¡b ) b¡1 ss ( 23) t a u eo oc pt r urmo e - se sc lr l .T h d lba d¯ a u e epa a t r b a dt o r me e s¿ n h seint e t r hev c o ° ,in ( 23)a ( nd 24)r spe t e y a e t e c iv l ,h v obec l a e . aibr t d Eq il r m u ib iu T h e u ibr m in t is e o o e q il iu h c n myis g e by( h iv n i)t eEul re u t n e q a io s, · ¸ ¢ 1 ¡ 1 ® = ¯E t 1 ¡± + ®z + 1 k ¡1 t t c c+ t ·t1 ¸ 1 c 1 t = ¯E t It c+ 1 ¦t 1 t + t a ur a st n r e o e us ¯ a ul ,o le n t e y oc pt e n a da d x g no sc lr e rat r a iv l 2 3 ²z t ru ¿t le = ° T 4 ²gt 5 ²I t ( 24) ( 25) ( 26) ( h r so r e c nst a t( 7 ,a ( ii)t e e u c o r in 1 ) nd iii)ase ft a sv r l y c n it n nto r n e sait o d io s,e su ingt tt et oa t in t is e o myr c iv ov l a io tt ndo he r ha h w sse s h c no e e en au t na hee ft l in o izo ft er pr se t t ea e t n r h s v l e te c nit ime iv gh r no h e e n a iv g n ,a da et u au da a h¯ et t , ¸ · tj 1 + k+ j = 0 ( ) 27 l Et ¯ im t j 1 ! c+ j t · ¸ 1 Btj + + l E t ¯t j im = 0 ( 28) j 1 ! c+ jP t j t + Eq a io ( u t n 28)g a a t e t au t n o o e n n u r n e s hev l a io fg v r me tbo s,a d ( )g a nd n 27 u r a t e c pit lst c v l a io .In u iv l , e u t n ( n e s a a o k au t n t it e y q a io 25)st t s t a h u il y a e h tt e t it pr v e by c n o id d o sumin o e u it o t g o t d y mu be e ua t t a o g n n f he o d o a st q l o ht f d v l pingao e pe io in e me tpr j c ,a d c n min o ro h tu it e eo n r d v st n o e t n o su gt mo r wt a n pl s t e be ¯ ft ein e me t u h ne to h v st n .Eq a io ( u t n 26)is t e Fish rr l t n be w e h e e a io t en in e e r t a d in a io h r a au o he inc e se in ut it g e by a t r st a e n ° t n;t e e lv l e ft ra il y iv n o e pe c n c e se in t da ' c nsu n r e tin r a o y s o mpt n mu io stbe e u lt t d o t d q a o he isc un e r a au o h o e pl s r a t r str t pe c n c e se t mo r wg e by e lv l e ft e n u e lin e e a e r e tin r a o r o iv n t d y s sa in ft is o e pe c n . o a ' v go h n re t 17 T h sou io o h mo e nd rc n e a io d a s t o c n it n le e l t n ft e d lu e o sid r t n ispl y w o d io a x pe t t n th r n o ,o o l e rf nc io s o h v r bl s in t e mo e . c a io s,a o izo ne fn n in a u t n ft e a ia e h dl O n f o e u t n ( ,a d a o he n f o ( .T od a it t m w w l e r m q a io 25) n n t ro e r m 26) e lw h he e il u h ppr a hinSims ( 0 0 )a dN o ae e l ( 999)o r a in a hc nd set ea o c 20 n v l s ta. 1 ft e t ge c o it n le pe t t na io a x c a io sane a ia ef rw ht l e h a io a x c a io s wv r bl o hic osov .T er t n le pe t t n e r r a c t d w h e c c nd io a x c a io c n be d ¯ e a r o s sso ia e it a h o it n le pe t t n a e n d s, · ¸ c¡1 1 c¡1 1 t t I ¡E t ( 29) »t = ¡1 c ¦t c ¦t t t · ¸ ¢ ¢ 1 ¡ 1 ¡ k ® ¡1 ® ¡1 »t = 1 ¡± + ®z k¡1 ¡E t 1 ¡± + ®z k¡1 ( ) 30 tt ¡1 tt c c t t T h r l o t e e pe t t n e r r w l be c u ia f r t e pu po s o t e oe f h se x c a io s r o s il rc l o h r se f he id n i¯ a io o sc lr v n s c mingfo t e¯ a l yr l . e t c t n f¯ a e e ue o r m h sc lpoic u e De e minist e d - a e tr icsta y st t T h mo lh s a w l- e n d st a y st t . F ra g e v r bl X t t e de a eld ¯ e ed ae o iv n a ia e , he st a st t sou io is t a e dy a e l t n h tpa t ul rsou io in w ic X t X t = X ss, 8 . r ic a l t n h h = ¡1 t G iv n Iss a d g ,w a o a h e d a esout nf o ( ,( ,( 7 , e n y ec n bt int est a yst t l io r m 25) 26) 1 ) ss ( 8) 22) 21 ) 1 9) 20 ) s w ul be e pe t d f o ( 1 ,( ,( ,( ,( .A o d x c e r m 29)a ( ) ss = 0 , nd 30 ,»I k »ss = 0 ,a w t¿ss le = 0 . nd ese ru 4. 2 M od els u on ol ti W esov l eal e ra o ima io ot emo e ,t a a in a ppr x t nt h d l h tc nbew it e r t nint eg n r l h e ea f r ( . Ti v c o ut is o size 1 1 £ 1i a d c mpo d o: c, b, It ¦t o m 6) he h t r e f , n o se f t t , , h ¡ ¢ ® ¡1 1 1 c t ,z ,g,¿t a d ¿t le ,alv r bl s a n ru l a ia e s E t c+ 1 ¦ t 1 ,E t c+ 1 1 ¡± + ®z + 1 k t t t t t + t d v t n f o it r spe t e st a y st t v l e e ia io s r m s e c iv e d a e au s.T h v c o fin o a io s," e e t ro n v t n , in l d s ²zt,²g a d²I .T h e t ro x c a io se r r t a w o cu e n t ev c o fe pe t t n r o s,´ ,h st oc mpo e t n n s: t I n k »t a d »t. T oo a q il ium t bt ine u ibr imese ie f ralt e1 3 v r bl s inut a d´t w a e rs o l h a ia e n eh v t eEu e o it n 25)a d( ; hed ¯ it nso h x c a io ro s,( h l rc nd io s( n 26) t e n io ft ee pe t t nse r r 29) a d( ) t e u c o st a to hea e t 1 7 ,a dt a ft eg v r me t n 30 ; her so r ec n r in ft g n s,( ) n h to h o e n n , ( 8) hee u t nspe if in h a st m ( ;t 1 ;t q a io c y gt et xsy e 22) hemo t r ne a ypoic ul 21 ) l yr e( ; t elw o h a s fmo io o h t c n l g a d pu icspe d gsh c , ( 9)a d ( ) t n ft e e h oo y n bl n in ok 1 n 20 r spe t e y n e c iv l ;a d,¯ al ,t et a e sait o d io s ( )a d ( . n ly h r nsv r l yc n it n 27 n 28) T h s, w h v 1 2 e u t n t sov f r1 3 v r bl s. T o f ly spe if t u e ae q a io s o l e o a ia e ul c y he ru sy e w a tbyse t st m est r t ing¿t le = 0 ,t e h npr c e it bse u n e u l e o e dw hsu q e tst pso tin d in t en x h e tsubse t n. c io 18 4 . I en ¯c ati 3 d ti onof m od el as ¯s alru e a -b ed c l Co r c ingt e e o e u ¯ a a il y c nd io nstu t h nd g no s sc lst b it o it n T h e in ov d in t ec mpu a io o h sc lr l a beilu r t d o est ps v l e h o t t n ft e¯ a u ec n l st a e n t e ba o h mo ld sc ibe in t is se t n.T o a h v t e d w h v h sis ft e de e r d h c io c ie e his n , e a e c o n t e st n a d c l a io sh w in T a e 1 . h se h a d r aibr t n o n bl T ab l 1: Calb rati e i on ¯ 1/ 0 .3 (1+ 0 5) ® 0 .6 3 ± 0 .2 5 0 Iss 1 + 0 .55 0 gss 0 .5 4 y ss ¿ss 1.4 4 0 gss ¿b 0 .4 / 0 . 0 4 ½z 0. 9 ¾z 0 .1 0 ½g 0. 9 ¾g 0 .1 0 ¾I 0 .1 0 T h pe sist n e pa a t r ½z a ½g , a d t e st n r de ia io s o he e r ec r me e s nd n h a da d v t n ft sh c s ¾²z , ¾²g a d ¾²I ha e be n c o n a bit a il , at o g t irv l s a e ok n v e h se r r r y lh u h he aue r co t h se c l a e in t e l e a u ef rt e U . e o o .A c mpl t n l se ot o aibr t d h it r t r o h S. c n my o e ea d q a t a iv in e pr t t n o h e o o u n it t e t r e a io ft e c n mic me n a ing o he n mbe s pr d c d ft u r oue be o l wis n tpr v e ,a w a e o l in e e e in t e q ait t e r su t o o id d s e r n y t r st d h u l a iv e ls.T he id n i¯ a io sc e e t c t n h meis impl me t d a f lo s. e n e s ol w In o rc se a d f rt e ba l e pa a t r t n,t e ma r P s t k s t u a , n o h sein r me e isa io h t ix a e he f r ( it c l mn l bes in l de f re seo e e e c ) o m w h ou a l cu d o a fr f r n e : 2 3 l c k b I ¦ W I W k g g ¿ ¿rue z P s =4 0 : 21 ¡ : 2 ¡ : 5 0 : 0 0 : 0 ¡ : 0 0 0 1 0 0 0 24 ¡ : 6 ¡ : 0 1 0 23 ¡ : 0 90 0 : 0 0 : 0 5 0 0 0:0 ¡:5 0 0 0 0:0 0:0 0:0 0 0 0 0:0 ¡: 0 0 83 ¡ : 0 48 0: 27 0 : 0 0 : 0 0 0 w il t e ma r r l t g e pe t t n e r r t r c u a o k f o ( he h t ix e a in x c a io s r o s ost u t r lsh c s, r m 9) £ s ¡1 ¤ ¡1 ¡1 P ¡ ¦ P s¡ ª = 0 0 · ¡: 0 64 ¡ 46 ¡ : 3 4: 0 0 ¡: 0 65 0: 36 0: 0 0 ¸ is, 19 A s al d d t a l r h t xr t r l be o s al a u c io o hec nlu e oe rie ,t e a a e u e c me ine rf n t n ft o 5 t mpo a o s sh c s a d l g e st t a ia e : e r ne u o k n a g d a ev r bl s ru ¿t le = 6: 34 g + 0 : 97 4652 zt+ 0 : 9 b¡1 ¡0 : 557k¡1 921 t 0 t t 4. 4 Som e i l s l trati res l u ve u ts So meilust a iv e ls o a e nt eba l r t er su t bt in do h siso h a io ft ev r uspo ssibil ie r e it sa epr se t d in A ppe dix 1 ,w h Fig r s 1 t summa isin her spo ne n it ue o3 r gt e nseo l c e fse e t d v r bl s in t emo e oash c a ia e h d lt o kint c noo y o e n n e h l g ,g v r me tspe d ga n in ndin e tr e a e r spe t e y T h impu se r spo se f c io s a e pr se t d f rt e str t s, e c iv l . e l e n un t n r e n e o hr e at r a iv spe i¯ a io s o h ¯ a u e ( ) t e tu st bil y c n it n o le n t e c c t n ft e sc lr l : i. h r e a it o d io s f t esy e h st m,a g e s iv nby( ,( )t 8) ii. hesc e h meo tin da v fe o e o sl aiu l e bo eo nd g n u yc l br t gt e¯ lr l ,a d( )ag n r o m o ne o e us r l o e e e e a in h sa u e n iii. e e icf r fa x g no u ef rr f r nc , a in ( .In t e ha t h v l e o b w s c o n sot a h t a e sait s 23) h sec r s,t e au f¿ a h se h tt e r nsv r l y c n it n o bo ds w u d h l G iv n t a h e e v l e a c t d t t o d io s n n o l od. e h tt e ig n au sso ia e o he 1 n au f¿ bo e 1 a h se me t n d c n it n is e u lt b ¡ ¯ ,a yv l e o b a v ¯ c n bec o n. n io e o d io q a o¿ In g n r l itis w r h n t e e a, o t o ingt tw e t e e o e o s r l is impo d t ha h n h x g n u u e se , he mo e l t n is in t r a e in t e se se t a e c n o sov f ralt d lsou io de e min t , h n h tw a n t l e o l he e pe t t nse r r x c a io r o sint emo l t a d»t.W eby sst h de:»I n k pa hispr bl m bya min o e ssu g I , impl ingt a I = 0 ;8 .T h is n t p re tf r sig ta r g r s t e e r r»t e fc o e h s e a d h ro y h t»t t is o n c ssa il na c r t e e r ya c u a eme ho oo yint ec n e to t d lg h o t x famo lw he pe t t n de it x c a io s, a w h v e fo t s e a ese n r m hest bil ya ay o hemo e . a it n l sis ft dl T h inf r t n in Fig r s 1 t 3 sh w ce ry t t t e pr pe t s o t e o ma io ue o o l a l ha h o rie f he simu a e pa h f rt e ¯ a a ia e in t e mo e r nsit e t her l l t d t s o h sc lv r bl s h d la ese iv ot u ese l c io .Inpa t u a ,t e nseo l c e a ia e t o h st l me t in et n r ic l r her spo fse e t dv r bl s ost c a ice e n s t e mo e o rat r a iv r l s a e c nsid r d in t e impu se r spo f n h d lf u l e n t e u e r o e e h se l e nse u c t ndia r ms:( )a io ga 1 nimpl itr spo sef nc io ,( ne pl itr spo sef n t n ic e n u t n 2)a x ic e n u c io ba do ne o e o sl aibr t d¯ a u ea d( se na nd g n u yc l a e sc lr l n 3)a\ st n r "r pr se t a da d e e n a t n o n e o e o sl io fa x g n u yimpo d ¯ a u e 6 se sc lr l . ²R e o sp nse t a tc noo y sh c ( u e 1 ) A c o t e t e at r a iv o e h lg o k Fig r : r ss h hr e le n t e f r l t n o h ue o mu a io s ft er l s,apo iv sit esho kt e h oo y( mo n in oa1 c ot c n l g a u t gt pe c n a epo td v t nf o it c n a tst a yst t au )h s w e y re t g in e ia io r m s o st n e d a ev l e a id l d e g n e l s f rg v r me td bta d t l sse e r e t x s.T he iv r e tr su t o o e n n e n , oa e rd g e , a e r a nf rt isd e in imepr ¯eo d u me tf rde e so o h i® r gt o l fa j st n o btisf iryst a h a l r ig t f r a d t t r e .W h r a t r a t n un e he e d g n u v r n s o w r oin e pr t e e s he e c io d rt n o e o s a ia t N o ic t a sh c s t t e in e e r t d n t pl y a r l in t e r l g e t irin n c n t e h t o k o h t r st a e o o a oe h u e iv n he sig i¯ a t e ima e e e to a e st t d ® c nt x s. 6 Spe i¯ al ,t er l a e t ef r c c ly h u et k s h o m: ¤ r e ¿tul = ¿b( t¡1 ¡b ) b 5 20 o h sc lr a t npr c ss is sh c - pe d n ,t eg n r x g n u ¯ ft e¯ a e c io oe o k de n e t h e e ice o e o s sc lr l t e t de ia io s o e r m it st a y st t t e sa r g r l ss a u e r a s v t n fd btf o s e d a e h me e a d e o h u c ft esh c .T h ® c s o ft eso r eo h o k ee e t fat c n l g e h oo ysh c n c pit la o ko a a c c umul t n f e t o g in ode a io e d hr u h t btw h t ee o e o s ¯ a u e he e it h x g n u sc lr l s,t r by ce t r a ingal g e r a t n o e ot t c n l g sh c .T h e a e a g d e c io fd btt he e h oo y o k is x mpl se v sa r e sau f lilu r t no h se u l st a io ft eimpo t nc fspe i¯ a io r a eo c c t nind t r e e minin y mic s t e v r ingspe d a d pr ¯e o dj me ta r ss r l s gd na s,a h a y e n o l fa ust n c o u e w ul in ic t .F rt e sou io w h a e o e o s r e t ispl y asimio d d a e o h l t n it n x g n u ul od a l rr spo set a e n oat c n l g e h oo ysh c s t etue st bil yc n it n o ka h r a it o d io ,ast o g rn r a t n is n e e ( b = 0 : ,w il aw a r a t n w u d l a t e c io edd ¿ 4) h e e k e c io o l e d oimpo r t n n pe sist n a ta d r e tde ia io s f o t e st a y st t , at o g pr se v g v t n r m h e d a e lh u h e r in st bil y a it .In o he o d t e dy a t rw r s, h n mic be v uro h e o e us r l is ha io ft e x g no u e h a il e nd n nt ec l a io ft espe do dj me tpa a t r e v yd pe e to h aibr t no h e fa ust n r me e . ²R e o sp nse t a g v r o o e nme ntsp nd e ingsh c Fig r 2) h d e in ® c s o k( u e :T e i® r ge e t o sh c t o e n n fa o k og v r me tspe ingw h r spe tt o e n n nd it e c og v r me tde btc no c r ma l t e r v r n o h v r bl t it st a y st t v l e a al en in y h e e sio ft is a ia e o s e d a e au , s l sh c s h v nimme t n o k a ea dia ea dsubst n ia ® c iv nse iv yo t r st a t le e tg e nsit it fin e e pa me t nde oma k tr t sint emo l o et tint y n so btt re ae h de.N t ha hispa t ul r ric a mo e h r a a ia e a e no ® c e by ag v r n d lt e e lv r bl s r ta e t d o e nme tspe d gsh c n in ok in t ea n eo n e pl it¯ a e c io f n t n s itis a r n r m h bse c fa x ic sc lr a t n u c io ,a ppa e tf o t epa e ft h n lo heFig r it u pu .T his is j stbe a set u ew ho t t u c u hesimpl emo e dl a ay dint is pa rpo sse R ic r nEq ae epr pe t s.Inmo e n l se h pe sse s a dia uiv l nc o rie r c mpl xa ic o e ndr hmo e sasot er a a ia e w u dbea e t d s sh w d l l h e lv r bl s o l ® c e ,a o n f rinst n e in M it h l ta. 20 0 0 ) o ac c e le l ( . ²R e o sp nse t n int r str t sh c Fig r 3) s in t oa e e a e o k( u e :A he¯ stt oc se n r w a s,a in e e a e sh c h s di® r t r str t o k a e inge e t d pe dingo t e r a t n pr c ss ®cs e n n h e c io oe in t x s a d de .T h a j st n o e in t e t ov r bl s is mo ae n bt e d u me tpr c ss h se w a ia e st sig c n l a e t d.A s w h a spe ingsho k sho k t t r str t s ni¯ a ty ® c e it nd c ,a c oin e e a e d e n th v n e le e t g e h o r ie o h l st a iv o s o a ea yr a ® c s iv nt epr pe t s ft eilu r t emo e . dl 5 Conl son c ui s T h pa rh s a t mpt d t is pe a t e e osho h t s a at r a iv oa e o e o sl wt a ,a n l e n t et n x g n u yimpo d c n io t g a a t e co e in t e ¯ a c o , a e do e u ¯ a se o dit n o u r n e l sur h sc lse t r n n g no s sc l co e r l c n be d r e o t e ba o h e ist g st u t r o ma r e l sur u e a e iv d n h sis ft e x in r c u e fa c o c n mic mo l A n ilu r t n o t me n by w ic a mo lba d ¯ a oo de. l st a io f he as h h de- se sc l r l c n be d r e w s c n a e in t e a ay o h ba mo e u l e ue a e iv d a o t in d h n l sis ft e sic d lo tin d in t l stse t n he a c io .In pr c e o e e ,t is me ho oo y is t a sf r bl t in ipl ,h w v r h t d lg r n e a e oa l r e n mo ec mpl x ma r e o micf r c st gmo e .A lh u h t e c ma g ra d r o e c o c no o e a in dl tog h o pl a e n t r o me o h l r e sc l mo e s c r n l ic t d a u e fso ft e a g - ae d l ure tyin u w u d r q ir se o l e u e ac r f limpl me t t n o h me h doo y o tin d h r ,t e ba a eu e n a io ft e t o l g u l e e e h sicpr c e in ipl s w u d r ma :ar e c n bed r e in e pl itf r o l e in ul a e iv d x ic o m,w r byt e¯ a u h r he e h sc la t o it r a t sy e t al t a v r t o o k y e c s st ma ic ly o a ie y fsh c s.W e sh w t a h pr se c o o h tt e e n e f 21 f r a d-o k ga e t o o w r l o in g n s,c mbine w h so o he d it me t rmil c n io s,is su ie t d o dit n ±c n t e t yau iq esa dl pa h l a in oast bl q ibr m. oid n if n u d e t e d gt a ee uil iu Th emo e - se u e o l dint ispa rsh r d lba dr l s utine h pe a ema yo h e a ef a n ft ed sir bl e t r s o x g n u y impo d r l s.M o u e fe o e o sl se u e stimpo t n l ,t e g a a t e sov nc r a ty h y u r n e l e y o t e pa to he g v r me ta r l o n h r ft o e n n nd u e utin r me tin a it .In a d io , st u n st bil y d it n te h ypo ss so sse mea dit na ppe l d io la aingpr pe t s n tsh r dbye o e o s ¯ a o rie o a e x g n u sc l r l s.Fir l ,t e r l s a e f r a d l o in .In t is r spe t h y a e c nsist n ue sty h u e r o w r - o k g h e c ,t e r o et w h t e spe i¯ a io o t rse t r in t ee o my o eg n r ly h r l s it h c c t n fo he c o s h c no .M r e e al ,t e u e a e c n e tw h t se u o h mo e r o sist n it he t p ft e d lin w ic t e a e impl me t d by h h hy r e ne , d sig , me ning t a c a g in st uc u a r me e s w la o t al be e n a h ta h n e r t r lpa a t r il ut ma ic ly r ° e t d in t e ¯ a u e Se o dl , t e a e st t - o t g n . Ex g n u y e ce h sc lr l . c n y h y r a e c n in e t o e o sl impo d ¯ a u e ma in ov a y l a e t r s, w e e f re a e a j st se sc lr l s y v l e c cic lf a u e h r , o x mpl , d u me to a e is d pe d n l l nt eo r e e ia io ft ed ¯ ito bt n ft x s e n e tsoe yo h bse v dd v t no h e c rde f o it t r e v l e T h e do e o s ¯ a ul s d r e h r , o t o he r m s a g t au . e n g n u sc lr e e iv d e e n he t r h n , a e c n e tw h t e se up o t e c o s in a r t n le pe t t nsa d r o sist n it h t fo h rse t r a io a x c a io ba d mo e .Co se u n l , t e a e aso sh c - c c in t e ® c s, w ic se dl n q e ty h y r l o k spe i¯ h ire e t h h is a d sir bl pr pe t f o a e o o e a e o ry r m n c n mic po t o v w A t a minimu t in f ie . m, he d r a io o t e pl it v r n o t se mo e - se r l s g e so g e iv t n f he x ic e sio f he d lba d u e iv s me uida c r g r in a o ia e f n t na o m o ¯ a ul .T h d y t r l s, n e e a d g ppr pr t u c io lf r fa sc lr e ir l , he u e in pr c e u h opr d c r l t ey smo t a u me tpr c sse f rt x s in ipl ,o g tt o u e e a iv l o h dj st n o e s o a e c n e t w h t c nsu o sist n it he o mpt n be v u fho h l w h c n a e u il y io ha io ro use ods it o c v t it fnt n u c io s.U n ik ma y e o e o sl impo d ¯ a u e h impu se r spo l e n x gn u y se sc lr l s,t e l e nse o a ia e is c n e t w h t e o ima t fv r bl s o sist n it h pt l ime pa h o d u me t o g n s t fa j st n fa e t w h t mo e , a d a j st n it in he d l n d u me tis n td pe de to e o e usl c l a e o e n n n x g no y aibr t d spe d o- d u me tpa a t r a l ,t ul s e e - fa j st n r me e s.L sty her e mbo dyo l c un e - y l a n y o t rc cic l a t ma ica j st n s o t e pa to h ¯ a u h r y u l ss ad r t n r u o t d u me t n h r ft e sc la t o it n e isc e io a y c mpo e tis a o nn ssume a dint is w yc nbec nsid r da aso to u o t d{ n h a a o ee s r fa t ma ic st bil t n a isa io . O n t e ba o o r ¯ ing t e e r ma se e a po h sis f u nd s, h r e in v r l ssibil ie f r f rhe it s o u t r w r .T h ok emo stin e e ingpo t r st ssibil yw u dbet x e it o l oe t ndt ea ay t h n l sis oamo e r c mpl xf a w r ,su ha al r e sc l o e r me o k c s a g - aema r e o o c o c n micf r c st o e a ingmo l he de .T d v l pme t o n o e o s ¯ a u e f re ist g l r e sc l ma r e o o e eo n fe d g n u sc lr l s o x in a g - ae c o c n mic mo e sw u dhep me su et ee e t e e ft ise o e us¯ a ul g in dl ol l a r h ® c iv n sso h nd g no sc lr ea a st t e r l s c r e ty in pr c ic . T his w u d aso al w f rw la e c mpa iso s h ue u r n l at e o l l lo o e f r o r n u de n rbo h t ee d g n u a d v r u e o e o s ¯ a u e t h n o e o s n a io s x g n u sc lr l s. 22 R ef erenes c A nd r n .S.( 0 0 ) A r l bl a c mpu a io al e ie tag r h f r e so ,G 20 ,\ eia e n o t t n ly ±c n l o it m o impo singt e sa l h dd epo tpr pe t in d na in o ry y micmo l ,M ime ,B o r o de s" o ad f G o e n r o heF d r lR e r eSy e v r o s ft e ea se v st m,Se e pt mbe . r A nd ¶ J. B al br aa dJ. al s ( 0 1 ) N o R ic r ia r s ,F. la ig n e V l¶ 20 e ,\ n- a d nFisc lP oic s in a l ie a O pe M o e a yU n " ime ,B a c n n n tr io ,M o n odeEspa a n a y 20 0 1 . n ,Ja u r ~ B a r l . Se t na dJ. ' e d( 994) Fisc lsov n ya d¯ a l y , r e lR ,J. f o n in tV l 1 ,\ a l e c n sc lpoic " N a io a st ut o o mica d So ia e a c D isc ssio P a r67 t n lIn it e fEc no n c lR se r h u n pe . B o n,H .( 998) T h be v uro . h 1 ,\ e ha io fU S.pu icde bl bta d d ¯ it ,Q u re l n e c s" a t ry Jo na fEc no s,949ur lo o mic 963. B r a tR .C.a d L .Z h n 1 996a ,\ In e t mpo a sc lpoic in ma r e o yn n a g( ) t re r l¯ a l y co c n micmo e s:In r d t n a d ma o le n t e ,D isc ssio P a rin o dl t o uc io n j rat r a iv s" u n pe In e na io lEc n mic 1 23,B r o in s Inst u io ,W a ing o D . t r t na o o s ok g it t n sh t n C. B r a tR . a yn C. ndL . ha ( 996b) A le n t espe i¯ a io s o t re Z ng 1 ,\ t r a iv c c t n fin e t mpo a rl ¯ a l yinasmalt e r t a sc lpoic l h o e ic lmo e " isc ssio a rinIn e n t n l d l ,D u nP pe t r a io a Ec n mic 1 24,B r o in s In it t n a in t n D . oo s o k g st u io ,W sh g o C. Ch r . . n a i,V V a dP. ho 1 999) O pt l¯ a ndmo t r Ke e( ,\ ima sc la ne a ypoic " a l y ,H nd b o fM a r e o mic 1 5 V ou o ko c o c no s l me1 c 67 - 7 ,1 1 1 45. Ch r .V . .Ch ist n n P.Ke o ( 994) O pt lFisc lP oic in a a i,V ,L r ia oa d he 1 ,\ ima a ly B usin ss Cy l M o l ,Jo r lo oit a o my 0 2,61 6e ce de" u na fP l ic lEc no ,1 652. Ch ist n ,L .a T .J.Fit e ad ( 0 0 ) U nd r a dingt e Fisc lT h o y r ia o nd zg r l 20 ,\ e st n h a er o h r eL e e " ft eP ic v l ,mime ,A pr o il20 0 0 . Ch r h K.B . P.R .M it h l,J.E.Sa l, K.F.W al ( 997 , \ Co uc , c el ut lis 1 ) mpa a iv rt e pr pe t s o o rie fmo e s o h U K e o o " N a io lInst ut Ec no d l ft e c n my , t na it e o mic R e ie ,1 61 ,91 - 0 0 . v w 1 Co h a eJ. . 20 0 1 ) L o - e m D e ndO pt lP oic c rn H ( ,\ ng T r bta ima l yint eFisc lT h h a e o yo heP r e L e e " o me r a r ft ic v l ,Ec no tic ,69( ) 1 ,69- 1 6. 1 de H a n .J.a d A .M a c t( 994) A c u a y in simu a io s" e ie f n a ,W n re 1 ,\ c r c l t n ,R v wo Ec no o micSt d s,61 ( ) 1 7 u ie 1 ,3- . F g n, G . J.H e y a d R .M e r ( 0 1 ) \ A n a e - id mo e A W M )f r aa , nr n st e 20 , r aw e d l( o t ee r r a ,ECB W o k gP a r42. h u oa e " r in pe G a r J.a d K.L .Jud ( 997 , \ Sov g l r e sc l r t n le pe t t n spa , n d 1 ) l in a g - ae a io a- x c a io s mo e s" a r e o mic Dy mic 1 ,45- 5. d l ,M c o c no s na s 7 H ug s H al t ,A . n M c d m,P. 1 999) nay s in M a r e o micM o he le t ad A a ( :A l se c o c no d e l .Kl w rA c d micP u ish r o d n ling u e ae bl e s,L n o . Jo so ,R . 20 0 0 ) A nimpl me t t no hec nst n - a ul hn n ( :\ e n a io ft o a tt xr einan ume ic l ra ma r mo e " M ime , F d r lR e r e B a k o co d l, o e ea se v n fKa sa Cit , N o e n s y v mbe r 20 0 0 . 23 Ju l r ila d,M . . a t n,P. c d m a dH . io o( 998) A nag r hm c m,D L x o M A a n P r 1 ,\ l o it o pe it n Fir - r e e a io s v r s N e t n ba d t c iq e , Jo r l t io : sto d rit r t n e su w o - se e hn u s" u na o o micDy mic a Co r l22,1 291 - 31 8. fEc no na s nd nto 1 Kil t ic ,A . 20 0 1 ) T r n r n r me o k sc lr l s a pa r k ( :\ a spa e tf a w r s,¯ a u e ndpoic - k g l y ma in u e nc ra t . a rpr se t d a a c It l h d W o k p o nd ru e t in y"P pe e n e tB n ad' aiaT ir r sho n P u icFin n e e u r 0 1 . bl a c ,F br a y20 L a t n . r ,P . a u e ,H . r sa ,E. ure bo m,B . 1 998) M U L x o ,D ,Isa d ,F r q e ,P a d ,T t l o ( :\ T IM O D M a kIII:T h o ed na r ec r y mica dst a y st t n e d - a emo l "O c a n l des. c sio a P a rN o1 64,In e n t n lM o e a yF n ,W a in t n D C. pe . t r a io a ntr u d sh g o L u a R .( 97 , \ Ec n me r P oic Ev l a io : A Cr iq " Jo na o c s, 1 6) o o t ic l y au t n it ue , ur l f M o tr ne a yEc no s,1 ( ,Su e n a ySe ie 1 97 9o mic 2) ppl me t r rs 6,1 46. L e pe , E.M .( 991 ) \ Eq il ia un e 'c iv 'a d ' ssiv 'mo t r a d e r 1 , u ibr d r a t e n pa e ne a y n ¯ a l ie ,Jo r lo o t r Ec no s 27( o e sc lpoic s" u na fM ne a y o mic N v mbe 991 ) 29r1 ,1 47 . M a c t A .a L o e zo G .( 999) \ T h pa a t r d e pe t t ns a re , nd r n ni, 1 : e r me e ise x c a io ppr a h o c :So pr c ic lissu s"in Co me a t a e mput t na a io lme h d f rt e st y o t o s o h ud f d na y mic e o mie Ed R .M a imo a A .Sc t , O x o d U n e sit c no s, s. r n nd ot fr iv r y P r ss. e M a imo , R .a d Sc t , A .( 999) Co r n n ot 1 : mput t na a io lme h d f r t e st d o to s o h u y f d na y mic e o mie c no s.O x o d U niv r yP r ss,O x o d fr e sit e fr. M c lu Cal m,B . . 20 0 1 ) Ind t r T ( :\ e e mina y bbl s,a h sc lt e r fpr e c ,bu e ndt e¯ a h o yo ic l v ld t r e e e e mina io "Jo na fM o t r t n. ur lo ne a yEc no s 47 1 ) 9- . o mic ( ,1 30 M c lu Cal m,B . . 1 999) Issu s int ed sig fmo e a ypoic u e "H a T ( :\ e h e no ntr l yr l s. nd b o fM a r e o mic 1 5 V ou o ko c o c no s l me1 c 483- 530 . ,1 1 M c Kibbin,W . ,Sa h J. c s,J. .( 991 ) G l ba ink g s:M a r e o o D 1 :\ o lL ae c o c n micIn e tr d pe e c a d Co pe a io in t e W o l Ec n my" B r o in s In it e nd n e n o rt n h rd o o . o k g st ut n a in t n D C. io ,W sh g o M it h l,P . . E. ul,K. W al ( 0 0 )\ Fisc lpoic u e in ma r e c e l R ,J. Sa t F. lis 20 a l yr l s co c n micmo e s:pr ipl s a dpr c ic "Ec no oo dl inc e n at e o micM o e l d ling1 7 7 - 93. ,1 1 1 M it h l,P. . E. ul,P. . c e l R ,J. Sa t N Smit ,K. W al 1 998) Co h F. lis( ,\ mpa in l ba r ggo l e o micmo e s" o micM o e l c no d l ,Ec no d ling1 5,1 48. N o ae A . D o g e v l s ,E. min u z,J. P ¶e n J. uiz ( 999) Sov gn n in a J. e z,a d R r 1 :\ l in o l e r r t n le pe t t n mo e s bye e v l e e e v c o e o a io a x c a io s dl ig n au - ig n e t rd c mpo io s"in sit n Co mput t na a io lme h d f rt e st d o y mic e o mie t o s o h u y fd na c no s,Ed s.R .M a r n a A . o t x o d U niv r yP r ss. imo nd Sc t ,O f r e sit e P ¶e e z,J. a dP. ie r 20 0 1 ) D e ninge d g n u ¯ a l yr l s f r r J. n H be t( ,\ sig n o e o s sc lpoic u e o ma r e o o c o c n micmo e s" ime ,Eu o a Ce t a a k d l ,M o r pe n n r lB n ,Jul 20 0 1 . y R o g rW .a d J.in tV e d ( 0 1 ) \ Q U EST :A mu t c u t y bu e c ce ee n ' l 20 , li- o n r sin ss y l a d g o t mo l" n r w h de .,Eu o a Co r pe n mmissio pa rII/ 5- - ,O c o r n pe 50 97 EN t be 1 997 . 24 Sims,C. . 20 0 0 ) Sov gl a a io a x c a io mo e s" ime ,Y ae A ( ,\ l in ine rr t n le pe t t ns d l ,M o l U niv r y e sit . Sims,C. . 1 994) A simpl A ( ,\ emo e o ud ft e e mina io ft epr e d lf rst yo hed t r t no h ic l v la hein e a t no e e ndt t r c io fmo t r n sc lpoic s" o micT h o y ne a ya d¯ a l ie ,Ec no er 4,489{ 494. W o d o d .( 995) P r e l v ld t r a y w h u h c n r lo mo o f r ,M 1 ,\ ic e e e e min c it o tt e o t o fa ne a y a g e a e , Ca ne ie R o h st rCo e e e Se ie o P ubic P oic t r g rg t" r g { ce e nf r nc r s n l ly 42,1 { 46. 25 Appendix 1 Figure 1. Alternative ways of building en endogenous fiscal rule Start with τ t rule =0 (i.e. “implicit rule” whereby agents adjust optimal plans to ensure stability) P s ut = 0 ⇔ (P Γ Π )η = (P Γ Ψ )ε s −1 0 s t −1 0 t τ trule = f (endogenous _ statest −1 , exogenous _ statest ) τ trule = γηt calibrate γ to replicate … extension: construct a “non-linear” version of τ trule Figure 2. Impulse reponses to a technology shock 0.5 Taxes, %deviations from steady state 0 -0.5 0.02 0 10 20 30 40 50 60 70 80 90 100 Output, %deviations from steady state 0.01 0 0.5 0 -0.5 -1 0.5 0 10 20 30 40 50 60 70 80 90 100 Inflation, %deviations from steady state 0 10 20 30 40 50 60 70 80 90 100 0 Debt, %deviations from steady state -0.5 0 10 20 30 40 50 60 70 80 90 100 Note: (i) The solid line corresponds to the solution based on the stability properties of the system; (ii) the dotted line to the "implicit" form of the rule; and (iii) the circles to the exogenous fiscal rule solution. (iii) the circles to the exogenous fiscal rule solution. Figure 3. Impulse reponses to a government spending shock 10 Taxes, %deviations from steady state 5 0 -5 1 Output, %deviations from steady state 0 0 10 20 30 40 50 60 70 80 90 100 -1 10 0 10 20 30 40 50 60 70 80 90 100 Inflation, %deviations from steady state 5 0 5 0 10 20 30 40 50 60 70 80 90 100 Debt, %deviations from steady state 0 -5 0 10 20 30 40 50 60 70 80 90 100 Note: (i) The solid line corresponds to the solution based on the stability properties of the system; (ii) the dotted line to the "implicit" form of the rule; and (iii) the circles to the exogenous fiscal rule solution. (iii) the circles to the exogenous fiscal rule solution. Figure 4. Impulse reponses to an interest rate shock 2 Taxes, %deviations from steady state 1 0 -1 1 Output, %deviations from steady state 0 0 10 20 30 40 50 60 70 80 90 100 -1 1 0 10 20 30 40 50 60 70 80 90 100 Inflation, %deviations from steady state 0.5 0 1 0 10 20 30 40 50 60 70 80 90 100 Debt, %deviations from steady state 0.5 0 -0.5 0 10 20 30 40 50 60 70 80 90 100 Note: (i) The solid line corresponds to the solution based on the stability properties of the system; (ii) the dotted line to the "implicit" form of the rule; and (iii) the circles to the exogenous fiscal rule solution. (iii) the circles to the exogenous fiscal rule solution.