Ev l a in h au t gt eCo s o u e Cy l s st fB sin ss ce d l fEn o e o s o t ¤ inM o es o d g n u G r wh G a i B a lv d re y D e rme to o o s pa t n fEc n mic N o t w st r U n e sit rh e e n iv r y 2003 Sh r a R o d e id n a Ev n o , IL 6 a st n 0208 e-ma :ba l y nw u il rev @ u.ed M a c 23, 2000 rh A bst a t rc In h f mo mo o r ph L u a (19 87 ) pu o t a a g is a us n ga , cs tf rh n r ume tt a h w la e g in n h tt e e f r a s f o r d c g t v l t it o a g e a e c n mpt n a e ne l ibl . Su q e t w r r m e u in he oa il y f g r g t o su io r gig e bse u n o k t a a r v e L u a ac l t n h s c n in e t h th s e isit d c s’c l u a io a o t u d o…n o l sma lbe e s f o r d c d ny l n …t r m e u - in t e v l t it o o su g h oa il y fc n mpt n f rh rr in o c g t e pe c pt n t a bu e c ce io , u t e e f r in h r e io h t sin ss y l s d n tma t r T h pa ra g e in e d t a o’ te . is pe r u s st a h t‡u t a io s c ul a e tt g o t pr c ss, c u t n o d ¤ c he r w h o e w ic c u d h v mu h l r e ¤ e t t a c n mpt n v l t it . I pr se ta a g me t h h o l a e c a g re c s h n o su io oa il y e n n ru n f rw y st bil t n c u d in r a g o t w h u o h a iza io o l c e se r w h it o ta r d c io in c r e tc n mpt n eut n u r n o su io , w ic c u dimpl bst n ia e f r ¤ e t a L u a (19 87 ) ar a yo r e h h ol ysu a t lw la ee c s s c s l e d bse v din h c l u- is ac l t n Empir a v e c a d c l a io e e c s su g stt tt e w la e e e t c n be a io . ic le id n e n aibr t n x r ise g e ha h e f r ¤ c s a q it bst n ia, po u esu a t l ssibl s mu h a t oo d r o ya c s w r e s fma n u eg e t rt n L u a r in l g it d r a e ha c s’o ig a e ima e st t s. ¤ T hea ho c no l dg s c mme t f o M a c a t o Sa Ko t ut ra k we e o ns rm r oB sse t , m r um, R o r uc s, A l xM o e H e e be tL a e ng , l ne R e , a se y nd mina rpa t ipa t a o t e e n, P ur ue U C B e k l y a U SC. r ic n s tN rw st r d , r e e , nd In r d c io to u t n In h f mo s mo o r ph L u a (19 8 7 ) putf r h a e e a ta g is a u n ga , cs o t n l g n r ume tt a h e f r ¤ e t n h tt ew la ee c s o sine c ce in t U n e St t s a e n gig e T h l g fh a g me tis a f lo s. fbu ss y l s he it d a e r e l ibl . e o ico is r u n s ol w Co side r pr se t t e c n me it a c n e t n lt -se r bl c nst n -r l t e r n ra e e n a iv o su rw h o v n io a ime pa a e o a t ea iv isk a e sio (CR R A ) u il yf c io vr n t it un t n 1 X C 1¡°¡1 t t ¯ t0 = 1 ¡° w e e° ¸0 . T his c nsume g e ac n mpt n st e m C t d …ne by hr o ris iv n o su io r a e d t C t= ( + Á) ( + ") 0 1 1 t C w e e Á r ‡e t a e a e c n mpt n g o t o e t hr e c s v r g o su io r w h v r ime a d " is a i.i.d r n m v r bl n t n . a do a ia e w hme nze oa dv r nc 2 t tc pt r s de ia io s o o sumpt nfo it t e dg o t it a r n a ia e¾ " ha a u e v t n fc n io r m s r n r w h r t . T h pa a t r Á a ¾ 2 c n be e ima e f o d t o l g pe -c pit c n ae e r me e s nd " a st t d r m a a n o r a a o sumpt n io f rt e U n e St t s o e h po -W o l W a o h it d a e v rt e st rd rII pe io T od t r e t e c st o g r g t r d. e e min h o s fa g e a e ‡u t t ns, L u a a s w a r c io finit lc n mpt nC 0 t is c n me o l c ua io c s sk h tfa t no ia o su io h o su rw u dbew l g ilin t sa r e in o d r t st bil his c n mpt n st e m, i.e t r pl c " w h it me n o c i…c r e o a ize o su io ra . o e a e t it s a E ( t 0 . F rr a n bl st t s o iska e sio , t ea sw rt r so tt ")= o e so a ee ima e fr v r n° h n e u n u obea o ish l st n ingy smal l ss t a 0 : %. B y c n r st c n me s w u d be w l g t sa r e a mu h l r e l: e h n 1 o t a , o su r o l ilin o c i…c c agr f a t n o it lc n r c io fin ia o sumpt n a ut20 % w n ° = 1 , in o d rt c e se t e g o t r t Á io , bo he r e oin r a h r w h a e byo epe c n a e po t n re t g in . V a io s a t o sha esinc e isit dL u a a c l t n, bu o h r u uh r v er v e c s’c l u a io tf rt emostpa tha ec n in e o r v o t u dt …n n ysmale e t f o st bil t n f r h rr in o c do l l ¤ c s r m a iza io , u t e e f r ingthepe c pt nt tbu ss c ce r e io ha sine y l s h v o l an gig e impa to w la e O n l e o t a kh s f c se o t e sho kpr c ss a e ny e l ibl c n ef r . e in fa t c a o u d n h c oe ". T h …r oma e t is a g t e stt k h r ume tw s Imr h r gu (19 8 9 ). She c it ize L u a ac l t n n a o oo l r ic s c s’c l u a io f rit impl ita mpt nt ta e t ha ea c ss t u lin r n e w hg r n e s t m t e o s ic ssu io ha g n s v c e of l su a c , hic ua a t e he h a e a e l v lo o v r g e e fc nsumpt n e c pe io Ifa g e a e sh c s d io a h r d. g r g t o k ono ¤ e ta e t u if r y ta c g n s n o ml a dc n mpt nin a c impe f c , t oa il yo a hind id ls c n n o su io sur n eis re t hev l t it fe c iv ua’ o sumpt nst e m io r a w ul be g e t rt a t e v l t it o pe c pit c nsu o d r a e h n h oa il y f r a a o mpt n ¾ 2 . B u w e Imr h r gu io " t hn o oo l c l a e in o st e ms t a ibr t s c me r a omic od t , sh …n s ac sto g r g t ‡u t t ns t tis no r aa e d o fa g e a e c ua io ha t mu h l r e ha L u a o ig a st t : o l 0 : c a g rt n c s’ r in le ima e n y 3% w e ° = 1 : M o e v r subse u n hn 5. ro e , qet pa r by A t e n a P hea (19 9 4) a d Kr se la d Smit (19 9 9 ) a g e t th rn t n o pe s k so nd ln n u l n h r u ha e o io f 1 st bil t n r mo e t o mu h idio n r t r f c d by a e t a o w h a g e a e r . a iza io e v s o c sy c a ic isk a e g n s l ng it g r g t isk T h y…n e dze oa de e n g t ebe e s t a iza io h n a g e a er r n v n e a iv n …t ost bil t nw e g r g t iskis st bil dina a ize a h tl a e h io n r t iskf c dbya e t un ¤ e t d.1 A n t rc it ism f c se o w yt a e v s t eid sy c a icr a e g n s a ce o he r ic ou s n t ef c ha he" pr c ss a me h a tt tt t o e ssu dinL u a ac l t nisn tsu¢c n l r e t Ifa e t c s’c l u a io o ie type sist n . gns h d t be rt e c n q e e o g r g t sh c s f re t nd d pe io s, t e w u d be mo e a o a h o se u nc s fa g e a e o k o x e e r d hy ol r a e set v r o‡u t a io s. T h a c l t n w e " f lo s ar n o w l it d if r e r e cu t n ec l u a io s h n t ol w a d m a kw h r ta er po t d inO bste d(19 9 4a F rpr f r n epa a t r t a r fl ). o e e e c r me e s h ta esimil rt h seu dbyL u a he…n s a ot o se c s, d c st o sine c ce t a r g in a u : 2 o s fbu ss y l s h ta ea a bo t0 3%. A se o d l e o t a k h s f c se o pr f r nc s, a g in CR R A u il y is t o r st ic iv c n in fa t c a o u d n e e e e r u g t it o e rt e a dc ul u d r st t h n o d n e e ima et ebe …t o a iza io . O bste d(19 9 4a c nsid r no x c e ne s fst bil t n fl ) o e s n-e pe t d u il y pr f r n e t t se r t be w e r -a e sio a d in e t mpo a su it t n B u t it e e e c s ha pa a e t e n isk v r n n t re r l bst u io . t o c g in, byO bste d s o n c r c e iza io t n ea a f l ’ w ha a t r t n, hew la ee e tr s f o amic o o ef r ¤ c ise r m r sc picl v l ee tome e y smal a d t e e ima e c str ma s be o %.3 P e rl l, n h st t d o e in l w1 mbe t n (19 9 6 a d D oma ro b) n l s (19 9 8 ) c n ra di¤ e e t ca o o -e pe t d u il y pr f r n e t a e hibit ‘ st r e ’ o side r n l ss fn n x c e t it ee e c s h t x …r -o d r riska e sio , a g in h tsu hpr f r n e c pt r bse v da t u e t w r s l r ea dsmal v r n r u gt a c e e e c s a u eo r e t it d s o a d a g n l be s t a r in o sist n it e pe t d u il y So o he st t s a e v r l r e bu t h ta e c n e tw h x c e t it . me ft ire ima e r e y a g , t o l un e t e a mpt n t a " is co t a u it r o . Ev n w n " is a t c re a e n y d r h ssu io h t t l se o n ot e he t u o orl td w h ½ = : D oma r po t t tt e c st o it 98, l s e r s ha h o s f‡u t a io s dono x e d 1 % f rr a n bl cu t n te c e o e so a e pa a t r t n Ex e sio so uc s’c l u a io h r f r e t o …r h r in lca r me e iza io s. t n n fL a a c l t nt e e o ese m oc n m iso ig a l im: t ec sto o su h o fc n mpt n v l t it r m c ce c l a e t io oa il yf o y l s a ibr t d opo -W a t t iv l st rda ais r ia . 1 Inapa a l lde t , Cl r , L e ie a r le ba e a k sl , ndSy ns (19 9 4) e ima et oa il yo mo st t hev l t it find idua iv linc mef o pa l o r m ne d t nd e ima e ac sto y l s a o a aa st t o fc ce r und 0 : % f rt U nit d King m. T his e ima eis simil ryc it ize by 9 o he e do st t a l r ic d Pembe t n (19 9 6) f rc un ingt r d t n o ro a o o t he e uc io fpur l id sy r t iska abe …to a iza io e y io nc a icr s ne fst bil t n. 2 B e ud y a P a e (19 9 9 ) c mbine t t o c it isms by st ing hig y pe sist ntidio nc a ic sho k a r nd g s o he w r ic udy hl r e sy r t c s. T he o a c st o a l a 1% . T his a o c se ms a pr mising w y t g ne a e mo e c sty busine y bt in o s f t e st ppr a h e o a o e rt r o l ss c ce e c lysinc he int o uc a iza io in aw yt td e no l y l s, spe ia l et y r d est bil t n a ha o s te imina eidio nc a icr . H o e e , t sy r t isk wv r t irmo e v ne a et uc s’o r a io t tift c st o he d lis ul r bl oL a bse v t n ha he o s f‡uc ua io st m f o inc mpl t t t ns e r m o e einsur nc , a e poic ma e s mig l y kr htbe be t ro pr mo inginsur nc r t rt n st bil t n. te ¤ o t a e a he ha a iza io 3 T al r (19 9 9 ) a g s t tO bste d’ pa a t r a einc nsist ntw h t q ypr mium. H eg ne a e a la ini r ue ha f l s r me e s r o e it hee uit e e r ts l r ec sto a g o fbusine c ce usingac e ie ss y l s o ¢c nto iska e sio ha o d r o fr v r nt tis r e s fma nit eg e t rt n O bste d g ud r a e ha fl . A simil rpo tis ma a in deinCa mpbe la Co hr ne(19 9 5) w l nd c a houseno t -se r bl e e e e t x a t n ime pa a epr f r nc s oe pl in he e uit e q ypr mium, a t ug t o l ho hO r k(19 9 9 ) a g s t tamo e“d ipl d c l a io fno pa a epr f r nc s r ue ha r isc ine ” a ibr t no n-se r bl e e e e g ne a e o ysma lw la ee e t T he r ume t no w hst nd , t q ypr mium do s no c ssa il e r t s nl l e f r ¤ c s. sea g n s t it a ing hee uit e e tne e r y impl l r e c st o y a g o s fbusine c ce Fir , t e uit pr mium c ul be d t ma k tf ic io ss y l s. st he q y e o d ue o r e r t ns. Se o , a c nd s A l a e ndJe ma v r za r nn(19 9 9 ) po into , t q ypr mium a ut hee uit e ndt o fc nsumpt n‡uc ua io a edist t hec sto o io t t ns r inc . T he st t a t rmo e o hema g lut it fc nsumpt nusing…na ia t ndputa ye ima eaf c o d lf rt r ina il yo o io nc lda aa nupperbo und o t o so n hec st fbusine c l s o : % . ss yce f0 3 2 T h pa r pur s a d e e t a o c t t c u d po e t ly g n r t mu h l r e c st is pe sue i¤ r n ppr a h ha o l t n ial e e a e c agr o s o busin ss c ce t n t e pr v u w r c e a v . It is mo iv t d by L u a o ig l f e y l s ha h e io s o k it d bo e t ae c s’ r ina o r a io ha v nsmalc a g s int r w hr t h v a g bse v t nt te e l hne heg o t a eÁ a el r eimpl a io sf rw la e A s ic t n o ef r . su h ifa g e a e‡uc ua io so h wa e t d a e a el n -r n g o t , t ec st o sin ss c, g rg t t t ns me o ¤ c e v r g o g u r w h h o s fbu e c ce c u dpo e t lybemu h l r e h n pr v u ye ima e . T his po y ls o l t n ial c a g rt a e io sl st t d ssibil yis r l do t it ue u by L uc s’t o g te pe ime t e t e t t e g o t r t Á a a e o e o s pa a t rt a a h u h x r n ;h r a s h r w h a e s n x gn u r me e h tis u a e t d by c a g s in " B u a d r mo e s o n o e o s g o t pr d tt e in e t e n ¤ ce hne . tst n a d d l fe d g n u r w h e ic h c n iv s o g n s t e a e in g o t -e h n in a t it s d pe d o t e l v lo c n mic a t it , fa e t o ng g r w h n a c g c iv ie e n n h e e fe o o c iv y sot tÁ = Á ( ) Ift is g o t r t Á ( )is c nc v , st bil t n w lin r a t e l n -r n ha ". h r wh a e " o a e a iza io il c e se h o g u g o t a eo o su r w hr t fc n mpt n Sinc v nsmalc a g sinÁ h v a g e f r o se ue c s, t is io . ee e l hne a el r ew la ec n q n e h c u dc n e a yg ne a ec st fbu e y l st a cipset sed sc ibe o l o c iv bl e r t o so sin ssc ce h te l ho e r dinpr v u o k e io sw r . T h t io ein uit nbe in h a g me tis ilust a e r ph a l h dt is r u n l r t dg a ic lyinFig r u e1. P r v us c l u a io s e io ac l t n me su et o so sin ssc ce a r hec st fbu e y l sbyc mpa in il yf o t eo r e oa il o sumpt n o r gut it r m h bse v dv l t ec n io st e m r pr se t d by t e he v l w h t e u il y f o a c n mpt n st e m se o t e ra e e n e h a y ine it h t it r m o su io r a tt h t e dr t ft eo ig lc n r n a eo h r ina o sumpt nst e m, a e e n e io r a sr pr se t dbyt h het insoidl e B yc n r st l in . o ta , ifst bil t na e t a e a eg o t , t ec sto a iza io ¤ c s v r g r w h h o fbusin ss c ce w lbet ed e e c e y l s il h i¤ r n einu il y t it f o t eo ig a o su r m h r in lc n mpt npa h a d fo t o su io t n r m hec n mpt npa hr pr se t d byt eda d io t e e ne h she l e Sinc h a t rpr v e mo ec n mpt n a a l rd t s, t eimpl d c st o sin ss in . et el t e o id s r o su io te rie a e h ie o s fbu e c ce c u dbesu a t la l n s a e t d y ls o l bst n ia s o ga g n s ono isc un h ut et oh a il . A c o d g td o tt ef ur o e v y c r in t h l g , t ema o o fbu e c ce is n tt a o sumpt n is v l t eo e ime a ot is o ic h j rc sto sin ss y l s o h tc n io oa il v rt , s h s be n st e d in pr v u w r , butt a a e r sse e io s o k h t‡uc ua io impe et t t ns d hepr c ss o r w h W hil o e fg o t . e t isid ah sbe no c sio a l isc sse h e a e c a n lyd u dinpr v u o k ith sy tt e io sw r , a e obein o po a e t h c r r t din ot e o ig lL u a f a w r in asa isf c o y w y4 T his is u o t n t , be a t e no io t t r ina c s r me o k t atr a. nf r u a e c use h t n ha st bil t nc nin r a r w ha a iza io a c e seg o t ndw la eisf rf o o io s. W h ta mpt n ef r a r m bv u a ssu io simpl ha yt t t e g o t r t Á is c n a e in t e l v lo c n mic a t it ? H o h r wh a e o cv h e e fe o o c iv y wmu h a d io a r w h c d it n lg o t sh u dw x c r m t ee imin t no y l a c u t n o l ee pe tf o h l a io fc cic l‡u t a io s?W il c ninc e seing o t lsu ha ra r wh 4 T he e is a r t rd use l e a ur w h a g s t tst bil t n y l be …t o he ha r duc d c n- r a he i¤ it r t e hic r ue ha a iza io ie ds ne s t rt n e e o sumpt nv l t it . F re a e D e o io oa il y o x mpl , L nga ndSumme s (19 8 8 ) a r ndR a ya me ndR a y(19 9 1) a g me r uest bil t n a iza io inc e se t l v lo ut , apo r a s he e e fo put intasor ise in Cha t r e a Co a (19 9 9 ). T his is d o e by R o r l a d t e je nd br e isc unt d me (19 9 6 w ), hoc e eit s vide e t tst bil t n is unl e y t ¤ e ta e a e o put M o e r c n o k st ie t nc ha a iza io ik l oa c v r g ut . r e e tw r ud s he e e t o a iza io o g o t usingmo e s o a t ra c ¤ c s fst bil t n n r w h d l ff c o c umul t n w h l a o uc io t c l g s. T his a io it ine rpr d t n e hnoo ie incud s A ize l e nma ndM a io na r n(19 9 3), H o nha na pe y ndM unia ur ia(19 9 6 deH e g r ), k(19 9 9 ), andJo s, M a ue l ne n li, andSt c he t (19 9 9 ), a w l s r l t dw r a c ti s e la e a e o kbyO bste d(19 9 4b) o heg o t fl nt r w hbe …t o l baiza io Exc pt ne s fgo l t n. e f rO bste d t sepa r a ec nc r d w h g o t p rse r t rt n w la e M o e v r t semo e s d o f l , he pe s r o e ne it r w h e a he ha e f r . r o e , he d l ono t me w l it t in uit n be sh e lw h he t io hind L uc s’w la e c l ul t ns, sinc f st rg o t in t ca o a e f r ac a io e a e r wh his l ss fmo e s do s dl e no tne e r y impl hig rw la e Fina l , R a y a R a y (19 9 5) a g t tv l t it a g o t a e c ssa il y he e f r . ly me nd me r ue ha oa il y nd r w h r ne a iv l e a e ba do mpir a v e ef o ac o c un r v e e B utw ho g t e yr l t d se ne ic le id nc r m r ss o t ye id nc . it utamo l t yc nno de , he a t in e pr tt pa a t r t y e ima e st uc ur ly f rw la ec l ul t ns. t r e he r me e s he st t r t a l o e f r a c a io 3 ln Ct t Figure 1: Consumption Paths under Endogenous Growth n c ssa il t a a e in oh h rw la e Ifso is ite ug t e r t l r e e f r e e t e e r y r nsl t t ig e e f r ? , no h og ne a e a g rw la e ¤ c s t a in pr v u w r ? hn e io s o k T o a r ss t se q e io I d v l p a mo e fe do e o s g o t in w ic sh c s a e t dd e he u st ns, e eo d lo n g n u r w h h h ok ¤ c t e l v lo c n mica t it . T he mo e e e a e ar d c d o m g o t r t Á = Á ( " ) h e e fe o o c iv y d lg n r t s e u e -f r r w h a e n( ), w e e n()is t e a u t o e u c s al c t d t in o a io a t it a d Á ()is t r t hr ¢ h mo n fr so r e lo a e o n v t n c iv y n ¢ he a e a h h be t rt c oo ie f rpr d c g g o a e d o e e f ra g e l v lo e u c s tw ic t e e hn l g s o o u in o ds r isc v r d o iv n e e fr so r e d v t dt e o e oinn v t n Se t g"t s e pe t d v l h r f r ¤ e t a e a eg o t h o g o a io . t in oit x c e auet e e o ea c s v r g r w ht r u h t oc nn l Fir , st bil t n c n in r a g o t by in r a gt e l v lo n v t n n w ha e s. st a iza io a c e se r w h c e sin h e e fin o a io , w ic il h hw lbet ec seifn()is c n a e Se o d st bil t nc nin r a r w h byr d c g h a ¢ o c v . c n , a iza io a c e seg o t e u in t e v l t it o , w ic w lbe t e c se ifÁ ()is c n a e P r v us w r o g o t un e h oa il y fn h h il h a ¢ o c v . e io o k n r wh d r u c ra t a n yc n e e h ste e t e e ho hitisw l n w h tt e a io sh n e t in yh so l o sid r dt e…r ¤ c , v nt ug elk o nt a her l t n ip be w e in e me ta u e t in y is a t e n v st n nd nc r a t mbig us, i.e n()c n be e h rc nc v o o v x uo . ¢ a it e o a e rc n e d pe dingo me h ta bit a yf nc io a o m a mpt n Ev nifst bil t n inc e se e n nso w a r r r u t n lf r ssu io s. e a iza io ra d a e a e in e me t t e impl a io s f r w la e r ma a v r g v st n , h ic t n o e f r e in mbig o s, sinc shif ing r so r e uu e t e ucs f o pr d c io t inn v t n ne d n tma e in id a s be t ro . T h se o d c a n l by r m o u t n o o a io e o k div u l t e ¤ e c n h n e, c n r st is mo ee u o a : dimin ingr t r s t no a io r q ir h tÁ ()bec n a e so o ta , r q iv c l ish e u n oin v t n e u et a ¢ o cv, st bil t n w lin r a g o t f o ag e l v lo e u c s n. F t e mo e t e in r a a iza io il c e se r w h r m iv n e e fr so r e urh r r , h c e se in g o t w la tt c e sew la e r w h il c oin r a ef r . T h a v d u n r ise t e q e io o o e bo e isc ssio a s h u st n fh wmu h g o t c u d be g n r t d f o d c r wh o l e e a e r m imin- ishingr t r s, a w t ritc n in ov su a t ly l r e ef r e e t t a t o t t e u n nd he he a v l e bst n ial a g rw la e ¤ c s h n h se ha c n be t a e t o a r c d oc nsumpt n v l t it . R e c d f r e ima e o t r l t n ip be w e io oa il y du e o m st t s n he e a io sh t en a e a e g o t a d t e v l t it o r w h ba d o c o o n r c mpa iso s su g st r - v r g r w h n h oa il y fg o t se n r ss-c u t y o r n ge s e mo in a g e a e ‡u t a io s in t e U .S. w u d r ise pe a a c n v g g rg t cu t n h ol a rc pit o sumpt n g o t fo io r w h r m 2: % t 2: 0 o 5%. T h in r a impl s a subst n ia o o is c e se ie a t lc st fbu e c ce w n ° = 1 , a sin ss y l s: he n in iv a o l be w l g t sa r e 1 0 % o d idu lw u d ilin o c i…c fhis in ia o it lc nsumpt n t st bil a g e a e io o a ize g r g t ‡u t t ns a d in r a l n -r n g o t , mo e t a 1 0 0 t s a mu h a L u a o ig al c ua io n c e se o g u r w h r hn ime s c s c s r in ly e ima e . U sin mpir a v e c o d st t d ge ic le id n e n imin in e u n t R &D fo mic ost d s c n ish gr t r s o rm r u ie o - …r t a v n c n r a iv e ima e f rdimin ingr t r s in t e pr du t n o e ms h te e o se v t e st t s o ish eun h o c io fn wid a es c ng n r t nin r a a e e a ea c e seint r w hr t f0 : pe c n a epo t H o e e , f r h rsc ut y heg o t a eo 5 r e t g in s. w v r u t e r in r v as t a h se e ima e a e ba d o f n t n lf r t a e u e impl u e v l t it e e l h tt e st t s r se n u c io a o ms h tr q ir a sibl oa il y in in e me ta d e u y v l s. St l r a n bl r st ic io o t e t n fv l t it pl c v st n n q it aue il, e so a e e r t ns n he x e to oa il y a e a u rbo n o ho n ppe u d n wmuc st bil t n c n in r a g o t t tis n tmuc l w rt a h a iza io a c e se r w h ha o h oe hn 4 t e r in le ima e h seo ig a st t s— r u h y2: o g l 3%, w his v l da ¡7 o hic aue t5 % finit lc n mpt n T h ia o su io . is su g st t a hedr ma icw la eimpl a io ba do e u e o m e ima e a ec n e t g e s h tt a t ef r ic t ns se nr d c df r st t s r o sist n w h pl u ea un s o imin it a sibl mo t fd ishin e u n gr t r s. Thepa ris o g n da f lo s. Se t n1 d v l ps t eba pe r a ize s ol w c io e eo h sicmo e fR &D w hd d lo it iminish g in r t r s t in v t n. Se t n 2 r l t s t mo e opr v u w r o st bil t n a e - e u n o no a io c io e a e his d lt e io s o k n a iza io nd n d g n u go t a o e o s r w h ndd in u e be w e ¤ e t o h e e fin e me ta dt ev l t it ist g ish s t e ne c s nt el v lo v st n n h oa il y o v st n . Se t n 3 e ima e t e size o t g o t e e t t a c n be a t ibu e t fin e me t c io st t s h f he r w h ¤ c s h t a tr t d o diminish gr t r s a d t e in e u n n h irimpl a io s f rw la e Se t n 4 c n l d s. ic t n o ef r . c io o cu e 1. A M o e fD imin h gR e u n t d lo is in t r s oIn o a io nvt n T ost d t e e t o u y he ¤ c s fbu e c ce o g o t , I n e a mo e fe d g n u g o t t t sin ss y l s n r w h ed d lo n o e o s r w h ha a mit ‡uc ua io in t e l v lo c n mica t it . M o e s o e h l g a no a io su h d s t t ns h e e fe o o c iv y d l ft c noo ic lin v t n c a G r ssma a d H e pma (19 9 1) a d A g io a d H o it s o n n l n n h n n w t(19 9 2) sa isf t c it r n T he t y his r e io . se mo e s h v w d l a et oimpo t n e t r s. Fir , t e ssu ra tf a u e st h ya meamo o l ic lyc mpe it ef a - n poist al o t iv r me w r w ic a l w f r di¤ e e t e u ibr m l v l o e o mic a t it . Se o d, c a g s in o k h h lo s o r n q il iu e es f c no c iv y cn hne eo o c n mica t it ¤ e tt ein e t e o g n s t n v t c iv ya c h c n iv s fa e t oin o a ebyc ng gt esizeo hema k t ha in h ft re amo poistc nc pt r no l a a u eifh c e d esu c e sinde e o gasu r rpr d c io e h iq e A ssu h v l pin pe io o u t nt c n u . c, a g e a e‡u t a io sw lh v nimpa to o g u r w h I in r d c g r g t c u t n il a ea c nl n -r ng o t . t o u e‡u t a io st r u h cu t n h o g sh c s t h c mpo io o o e n n o k ot e o sit n fg v r me tspe in . T h c o e is mo iv t d t nd g is h ic t a e ominimize t e h n mbe fa x ia y mo e l u ro u il r d linga mpt ns t a e e a e my r su t no ssu io h tg n r t e l s, tbe a se I v wt e cu ie h c mpo io o o e n n o sit n fg v r me tspe ding a a impo t n u c o g r g t ‡u t a io s. U li- n s n ra tso r e fa g e a e c u t n t ma e y t e w la e e e t I e a e o c rbe a se st bil t n r d c s in e me tv l t it . t l , h e f r ¤ c s x min c u cu a iza io e u e v st n oa il y T h mee e t c u da isein a ye v o esa ¤ cs o l r n n ir nme tw r n v t n ‡u t a e o e imea d t e n he ein o a io c u t s v rt n h u de l in pr d t n f n t n f rn w id a is c n a e in f c , t e n x c io ilu r t s n ry g o uc io u c io o e es o cv; a t h e tse t n l st a e simil re e t in a mo e h r t e so r e o a ¤ cs d lw e e h u c f‡u t a io s c n be in e pr t d a t c n l g cu t n a t r e e s e h oo y sh c s. Sinc t e so r e o g r g t ‡u t a io s d e n tpl y a r l in my su q n t ok e h u c fa g e a e c u t n o s o a oe bse ue ta - t mpt a u n if in h e f r ¤ e t o a iza io , t e s tq a t y gt ew la ee c s fst bil t n hepr c e isew yin w ic I mo e a h h d litis u impo t n .5 T hemo e pr se t d in t opa t T h stpa td sc ibe it ma f a u e n ra t d lis e n e w rs. e…r r e r s s in e t r s, 5 A l ho h t t ug heso c fa g e a e‡uc ua io ha nobe r ur eo g r g t t t ns s a ingo t n heq st n o he he ue io fw t rbusine c l s c n ss yce a ha e …r r e e f r c st itr ma c uc lf rd t r v sto d rw la e o s, e ins r ia o e e mining t f ahe e sibil y a c sto a iza io w h it nd o fst bil t n, hic ul ima e yde e mine w t rst bil t n is d sir bl . B utt t tl tr s he he a iza io e a e hepo to his pa rt ha l ng heno io t t in ft pe oc le et t n ha busine c ce ha e no…r r rw la e e e t no oa g in f v ro a iza io ss y l s v sto de e f r ¤ c s, tt r ue a o fst bil t n. 5 w il t c n h r c e ize s q il ium.6 h e hese o d c a a t r s it e u ibr 1.1. Se u tp T h c n myc n a s t r e a e t ee o o o t in h e g n s: 1. A r pr se t t ea e t w oc n me g o s a d su ie l bo e e n a iv g n , h o su s o d n ppl s a r 2. A g v r me t w h t x s t ea e ta d spe d t e r v n eitc le t o e n n , hic a e h g n n n s h eeu ol c s 3. En r pr ne r w oh el bo opr d c o d a d t e e o n wpr d c io me h d t e e u s, h ir a rt o u eg o s n od v l p e o ut n to s Itw lbe h l u o pr v w t e r spe t e r l s o h v r u pa t s. T h a e tpl y a il e pf lt e ie h e c iv oe ft e a io s rie e gn a s n impo t n ra tbutpa e r l : h c n ssiv oe e o sume o t t w ic pr v s u w h a w la e me su e s u pu , h h o ide s it ef r a r t c mpa e d e e t e o o o o r i¤ r n c n mic e v o n ir nme t T h g v r me t a n t d a v , a t a t e n s. e o e n n , s o e bo e c s s h so r e o c u t n a d c n be use t t o uc st bil t n in ot e mo e . T h r l o u c f‡u t a io s, n a d oin r d e a iza io t h dl e oe f e t e e e r a e f o pr d ing o t t is t d v l p be t rpr d c io me h d T h n r pr n u s, sid r m o uc u pu , o e eo t e o u t n t o s. is, in t r d t r e t g o t r t f rt e e o o . T h u t t g a ft e mo e u n, e e min s he r w h a e o h c n my e lima e o lo h d lis to g ug o a eh wbusin ss c ce a e tt ed c n o n r pr n ur t a r utinn v t n a dt e e y l s ¤ c h e isio s fe t e e e s oc ryo o a io , n h c n q n e t is h s o t ew la e o h r pr se t t e a e t o se ue c s h a n h e f r ft e e e n a iv g n . I n wd sc ibe t e t r e a e t in mo e d t il Fir , t e r pr se t t e a e th s st n a d o e r h he gns r ea . st h e e n a iv g n a a d r CR R A pr f r nc s o e e e e e v rac n o sumpt n a g e a e i.e h ut it tad t is g e by io g r g t , . is il ya a et iv n 1¡° C t ¡1 U (t C )= 1 ¡° w e e° ¸0 a d C t is aCo hr n bb-D o ga a g e a o v rc n mpt n g o s c t f rj 2 [0 ;1 ] u l s g r g t ro e o su io o d j o : · 1 Z ¸ C t= e p x l jd nc t j 0 T ime is c n in o s, a d t g n a e a uth e pe t d d o n e u il y o t u u n hea e tc r s bo is x c e isc u t d t it Z1 C ) ¡½t t U ( te d 0 6 Sinc w it t pa r I ha e be o a a e o r l t d mo e e r ing his pe , v c me w r fa e a e d lby Fa a (19 9 8 ). A sid f o d e ingin ts e r m i¤ r c r a d t il f o t mo e , hef c s o di¤ e e tq st ns. e t in e a s r m his dl o use n r n ue io 6 w e e ½ > 0 is h disc u t r t . I c o se CR R A ut it d spit it dr w c s w ic a e hr is o n ae ho il y e e s a ba k h h r d u d in t e In r du t n h se c n e n a t u t w r r , w h is n timpo t n o isc sse h t o c io ;t e o c r t it de o a ds isk hic o r a tf r my a a y n l sis. F rt is r a n ° sho d be v w d a a me sur o t r e o h e so , ul ie e s a e fin e t mpo a bst ut n r lsu it io r t e ha ame su e o isk v r n. a h rt n a r fr -a e sio T h a e tis e o e w h L u it o a re c inst n . L e r d e no n e is u il y e gn nd w d it n s fl bo a h at isu e o s te t rh t it f n t n so h su ie alo is l bo he e e he w g is po iv . T he a e taso o n u c io , e ppl s l fh a rw n v rt ae sit e gn l w s alca l l ims o t e pr …t o n r pr n u s in t is e o o , po iv a n g t e F lo in n h o s fe t e e e r h c n my sit e nd e a iv . ol w g L uc s, I init ly a r c r m sa in s;t e a e tmu o su alo a ia l bst a tf o v g h gn stc n me l fhis dispo bl in o , sa e c me w ic is t esu o a rin o h h h m fl bo c mea d pr …t n to a ia it s. H o e e , t is a mpt n is n o s e ft xl bil ie w v r h ssu io n timpo t n , a is d mo st a e in Se t n 2 w e e I de iv simil rr su t f ramo e it o ra t s e n rtd c io hr r e a e ls o d lw h sa in s. Int ea n eo v g t eo l h ic h g n v g h bse c fsa in , h n yc o et ea e tma e is ho oal c t is in o ks wt lo a eh c me a r ss d e e tg o s. Sin e C t is aCo c o i¤ r n o d c bb-D o ga a g e a o , itis o ima ospe d a e ua u l s g rg t r pt lt n n q l a un n e c g o j 2 [0 ;1 ] In e r t go e l o d impl s t spe d gr t o e c mo to a h o d . t g a in v ralg o s ie he n in a e n a h g o j is t e sa od h mea d s ispo bl c me sa ein o , Z1 pj j = c pj j j = ¦+ W ¡T cd 0 w e e¦ d n t s a g e a epr …t W d no e l bo hr e o e g r g t o s, e t s a rinc me a d T d n t s t xl bil ie L e o , n e o e a ia it s. t Y ´¦+ W d n t g o n mina c me e o e r ss o lin o . N e t I t r t t g v r me tse t r G o e nme tt x s t e l bo c me o h a e ta d x, u n o he o e n n c o . v r n a e h a rin o ft e g n n u s t is r v n e t se h e e u o…n nc v r u e pe d u e T h t x r t is ac n a t¿ 2 ( ;1 ) Sinc a e a io s x n it r s. e a ae o st n 0 . e l bo a rsuppl is inea ic t is t x is e u ae tt y l st , h a q iv l n oal ump-su t x H o e e , t e f c h tt e m a. w v r h a tt a h t xis pr po t n lt a rinc meis impo t n , sin eital w g v r me tr v n og o s a o r io a ol bo o ra t c lo s o e n n e e uet r wa l bo e u c sbe o a rr so r e c memo epr d c iv . W it o tt isa mpt n, g v r me tsh r fo t t r out e h u h ssu io o e n n a eo u pu w ul e e t al a ish. In w a ol w I u l bo s t e n me a e g o . T h t x r v n e o d v n u lyv n h tf lo s, se a ra h u r ir o d e a eeu in e c inst n ah a tis t e e o e T = ¿L . I a me t e bud e h rf r ssu h g tis baa c d a a h inst n , i.e t e l n e te c at . h e t e r v n e T is a w y spe to c c le t d. T h r v n pa s f rg o t g v r me t n ir e e u l as n n e ol c e is e e ue y o o ds he o e n n c n me a d f rw r e s t eg v r me th e H e c , o su s, n o o k r h o e n n ir s. n e T = G t+ N t w e e G t de o e g v r me tspe in o g o s a N t d n t s t e t t lw g bil fg v hr n ts o e n n nd g n o d nd e o e h o a a e lo o - e n n e o e s. G iv n t e n r l t n t a a ris t e n r me t mpl y e e h o maiza io h tl bo h ume a e t e l t e r ir , h a t ris aso l t en mbe fw r e s e o e byt eg v r me t T h no a io mig tbeal tec n u g h u ro o k r mpl y d h oen n. is t t n h it l o f sin 7 a st e c ly sin e G t is a n min lq a t y w il C t is a r a ua t y H o e e , itis t…r , spe ial c o a u n it h e e lq n it . wv r c n e ie tt w r w h n mina u n it s in sov g t e mo e , e e t o g w u t t l o v n n o o k it o lq a t ie l in h d l v n h u h e lima e y R c r bo tr a o mpt n I d n t o a o sumpt n byP t t´ 01 pj c t a ea u e lc nsu io . e o en min lc n io C t j. G o e n n e pe it r s o g o a e a v r me t x nd u e n o ds r ssume t be al c t d e u ly a r ss t e d e e t d o lo a e q a l c o h i¤ r n c mmo it s j 2 [0 ;1 ] i.e spe d go e c g o j a a et is t esa o d ie , . n in n a h o d td t h mea u tg r g r l ss mo n t e a d e o he pr e o h tg o Itf lo s t a g r g t g v r n ft ic ft a o d. ol w h ta g e a e o e nme tspe ingo g o is e u lt nd n o ds qa o g, sin e t c Z1 G t= gd = g tj t 0 B u d go M a su a il in n t y ma(19 9 5), I a me t e g v r me tma t in ac n a tt x c le t n ssu h oen n in a s o st n a ol c io T butpe io ic ly sh t t e c mpo io o r d al ifs h o sit n fspe ding be w e g o s a d l bo . Spe i…c ly n t en od n a r c al , a g e a e g v r me te pe it r s G t c n a me o e o w v l e G 1 > G 0 , a d sw c g r g t o e n n x nd u e a ssu n ft o au s, n it h be w e t se t o v l s a a r t ¹ pe u it o t . D e o e t e a c t d n mbe o t e n he w aue t ae r n f ime n t h sso ia e u r f g v r me tw r e s e o e in e c r g o e n n o k r mpl y d a h e ime byN 0 = T ¡G 0 a d N 1 = T ¡G 1, r spe t e y n e c iv l . B u e ba a e impl s N dg t l nc ie 0 > N 1 , i.e mo e w r e s c n w r in t e pr a e se t r w n . r ok r a ok h iv t c o he g v r me tsh t it spe in o a d g o s. o e n n ifs s nd gt w r s o d Sh t in t o if s hec mpo io o o e n n sit n fg v r me tspe din e e a e a g e a e ‡uc u t n in t c n n gg n r t g r g t t a io s hee o - o . T h is be a seinc e se o e n n my is cu r a dg v r me tspe ingo o d sh t l bo e u c s o ft e nd ng o s if s a rr so r e uto h g v r me tse t ra d in o t e publ se t r B e a o e n n co n t h ic c o . c use ofmo poist c mpe it n w r e s no l ic o t io , o k r gn rt e e a emo ev l ew r inginpr d c io h nw r in o h o e n n : int el t e , t e r au o k o u t nt a o k gf rt eg v r me t h a tr h y o l g ne a e l bo c me w il in t f r rt y g ne a e bo h l bo c me a pr …t n y e r t a rin o , h e he o me he e r t t a rin o nd o s. H e e a sh tin t c mpo io o o e n n nc , if he o sit n fg v r me tspe d g t w r g o s r ise t e v l e o n in o a ds o d a s h a u f l bo e u c s in t e o my w ic in t r a e t t e sc l o o c io in t e e o o . a rr so r e his c no , h h u n ¤ c s h ae fpr du t n h c n my Final , I t r oe t e e u s. T h ypr du et ev r u g o s j 2 [0 ;1 ] a w l s se r h g ly u nt n r pr ne r e o c h a io s o d , s ela a c in f rbe t rw y o o u in h se g o s. In bo h c pa it s, t e a e d iv n by pr …tma i- o t e a s fpr d c gt e o d t a c ie h y r r e o x miza io T h n t r o o uc io in t is e o my is a f lo s. Ea h g o j is a c t d t n. e a u e fpr d t n h c no s ol w c od sso ia e w h a n mbe j t a e c s t e h he e r t n o e h l g a a a e f rpr d c g it u rm h tr ‡e t h ig stg ne a io ft c noo y v il bl o o u in t a o d P u no h rw y mj is t e n h tg o . ta t e a , h umbe ft s t t c n l g f rpr du in o d j ro ime he e h oo y o o c gg o h s be n impr v d u n sin e d t t = 0 . Ea h g n r t n c n e t l bo t o pu ta a e o e po c ae c e e a io o v r s a rin o ut ta l e rr t , bu c e e g n r t n a e mo e pr du t e Spe i…c ly t e m-t g n r t n in a a e tsu c ssiv e e a io s r r o c iv . c al , h h e e a io e h oo y lo s ne nito a rt o c ¸ m u it o u pu , w e e ¸ > 1 is t e r t o t c n l g al w o u fl bo opr du e n s fo t t h r h ae f 8 pr g e a c t d w h e c impr v me t T e hn l g s a e pr t c e by ind …nit pa e t o r ss sso ia e it a h o e n . c oo ie r o e t d e e t n s, soo l t e c e t ro he m-t g ne a io t c n l g c n u itt o uc g o s. St l t e n y h r a o ft h e r t n e h oo y a se opr d e o d il, h d v l pme to h e eo n ft em-t g n r t n al w o h re t e e e s t e eo t em + 1 -t g n r h e e a io lo s t e n r pr n ur od v l p h h e e- a io , sod o e in t n isc v r gan wpr d c io e h ueheps bo ht ein o a o hod o e s ita d e o u t nt c niq l t h n v t rw isc v r n h c mpe it r is o t o s. I …rstde r e t e e u s in t e a c y a pr d c r Ea h e t e e e rw lpr d e sc ibe n r pr ne r h irc pa it s o u e s. c n r pr n u il o uc u g t e hig e e e a io h ha a c ss t . H is o l r a e isio is w a ic t c r e sin h h stg n r t n e s c e o n y e ld c n h tpr e o ha g f rhis g o . Sin e bo h c nsu ra g v r me tspe d g o e c g o a e ind pe d n o od c t o me nd o e n n n in n a h o d r e net o h pr e d ma d f re c g o is u ft e ic , e n o a h o d nite a ic Ea h mo o l l st . c n poistw lt e e o e w n ose il h r f r a tt t a h h apr e a po s ig ic s ssibl ;t w y h e r s t e sa r v n bu a pr d c f w rg o s. e his a , e a n h me e e ue tc n o u e e e o d B u e c nn tpo th a o stapr e t tis t oh h;ifh pr e e c e s t c sto o u in ic ha o ig is ic x e d he o fpr d c gasin l ge u ito is ne tmo ¢c n o n fh x ste ie tc mpe it r t e l t e il sta sl h l l w rpr e a d st a t o , h a t rw lpo ig ty o e ic n e l a a a lo is bu ss. H e c , pr d c r q t a pr e e u lt t e ma g a o ft e w y l fh sine n e o u e s uo e ic q a o h r in lc sto h ir mo ¢c n o ste ie tc mpe it r a d t e e t e e e rw h t h h stg n r t n o e h l g il t o , n h n r pr n u it he ig e e e a io ft c noo yw l be t e o e suppl in g o s t t e ma k t T his impl s t ta e t e e e rw h t e m-t h n y g od o h re. ie ha n n r pr n u it h h e e a io e hn l g il this pr epj t ¡(m ¡1): his n x g n r t n t c oo yw lse ic o¸ e tmo ¢c n o ste ie tc mpe it rn e s t o ed ¸ ¡(m ¡1) w r e s t o uc o o k r opr d e neunito u put a d e c w r e pa aw g n r l d t fo t , n a h o k ris id a e o maize o 1 . A tt is pr e t u h ic , hen mbe fu s t emo o l ro nit h n poistw lse lis g e by il l iv n Y ¡T + G = ¸m ¡1 ( ¡T + G ) Y (1.1) pj T o pr d c e c o h se un s, h n e s t h e ¸ ¡m u s o a r H e e h t t ll bo o u e a h ft e it e e d o ir nit fl bo . nc , is o a a r r q ir me tis g e by ¸ ¡1 ( ¡T + G ) W it l bo s t e n me a e t is asot e t t l eu e n iv n Y . h a ra h u r ir , his l h oa c sto o c gt eq a t yin (1.1). H is pr …t w lt e e u lh r v n ene fc st o o fpr du in h u n it o s il h n q a is e e u to o s, r 1 ¼ = pj j¡ ( ¡T + G ) c Y ¸ ¸ ¡1 = ( ¡T + G ) Y (1.2) ¸ In w a ol w I r st ic t e t n t a k v e uil iain w ic n mina c me Y de n s h tf lo s, e r ta t n io oM r o q ibr h h o lin o pe d o l nt el v lo o e n n n yo h e e fg v r me tspe in ;itisa pe nd gG no nissu st h t e t re u ibr l ea ow e h ro he q il iaaso e ist In su h a e uil iu pr …t ¼ w ld pe o l o t e l v lo o e n n x . c n q ibr m, o s il e nd n y n h e e fg v r me tspe ing nd . L e 0 d no epr …t w e G = G 0 a ¼ 1 w e G = G 1 . t¼ e t o s h n nd hn Final , I d sc ibe e t e e e r in t e a c y a in v t r I a me t e e a e o l t o ly e r n r pr n u s h irc pa it s no a o s. ssu h r r ny w e t e e e r in se t rj a n po tin t : o w oo ns t pa e tt h be v il bl n r pr n u s co ta y in ime ne h w he t n ot e sta a a e 9 tc n l g n e h oo ya dpr d c so t , a h t e h a o ko o u e u put ndt eo h rw oc nw r nde e o gabe t rt c n l g v l pin t e e h oo y f r pr du in t is g o . P r v u w r h s a o d h v o o c g h od e io s o k a v ide a ing t ma e su h a mpt n by o k c ssu io s imposingc n a tr t r t aeinr se r hao gw hf e n r . Int is c se t u o st n e u ns osc l e a c l n it r ee t y h a , hen mbe f ro po e t le t a t d e n tma t r a a inc mbe tmo o l t n ia n r n s o s o t e , nd n u n n poistw ln v rc o se t ng g il e e h o oe a e inr se r hine u ibr m. T oa l wf rdimin ingr t r s t her se r he o t o e ac q il iu lo o ish e u n ot e a c ¤ r s find id l iv ua ed o se he ssumpt n e pl ity7 Ift e t e e e rin a g e e t e e e r I n e t impo t se a n r pr n u s, io s x ic l . he n r pr n u iv n se t rw oe g g s inr se r he o s n w r e s, hed o e s t e tg ne a io t c n l g co h n a e e a c mpl y ok r isc v r hen x e r t n e h oo y ( j+ 1 )a m tar t ( a eÁ n)pe n ft . T h un t n Á ( )is st ic l c e sin n c n a e ru ito ime ef c io n r tyin r a ga d o c v , t s h su lbo d r c n it n l Á 0( a d sa is…e t e u a n un a y o d io s im n)= 1 a d l Á 0( n im n)= 0 . Co c v y n a it n! 0 n! 1 in Á ( )is a c t d w h d n sso ia e it iminish gr t r s in r se r h a d v l pme t t e c n r io in e u n e a c nd e e o n : h o t ibut n o h ma g a o k rt t e pr ba it o ft e r in lw r e o h o bil y fsuc e d c e se w h e c a dit na w r e . c ss e r a s it a h d io l o k r D e o in h v l e o su c ssf linn v t n by v, t e inn v t rs pr bl m is t h o n t n t gt e a u fa c e u o a io h o ao’ o e oc o se o ma imizeÁ ( ) ¡n, so x nv Á 0( ) = 1 nv (1.3) 1.2. E u ibr m q il iu W it t e d sc ipt n o h e o my c mpl t , I c n c a a t r it e u ibr m. T h is j st h h e r io ft e c no o ee a h r c e ize s q il iu is u ase fpr e a d q a t ie a a h in a tsu h t t(1) a e t c o se pr e a q n it s to ic s n u n it s te c st n c ha gns h o ic s nd ua t ie o imal ;(2) t o e n n pt ly heg v r me tbu g tis ba a e ;a d (3) o t ta l bo de l nc d n u pu nd a rma k t ce r A s r e s la. n t d be o e I f c s o M a k ve uil iain w ic n min lv r bl s v r n yw h t e l v l oe f r, o u n r o q ibr h h o a a ia e a yo l it h e e o oen n fg v r me tspe din . Itw lh l t n g il e p opo to ta h st g h sef a u e o n e u ibr m in u tt is a et o e t r s fa q il iu w ic h v a c u t r r t L u a spe i…c t n f r c nsu h h ae o n e pa t o c s’ c a io o o mpt n Fir , a e uil iu is io . st n q ibr m a c t d w h al v lo o se l c n mpt n a a h in a t G iv n a h o y u t a e sso ia e it e e fh u hod o su io te c st n . e ist r p od t t h u h l c n mpt n a a e t t k s o di¤ e e tv l e de nd go t e r aiza io G t , o se od o su io td t ae n r n au s pe in n h e l t n . Co su n mpt n c n t r f r be a v o l wit e pe t d v l e w ic is a ao o t h " io a he e o e bo e rbe o s x c e au , h h n l g us ot e t r in L u a em c s’spe i…c t n Se o , a e uil iu is a c t d w h a l v lo mpl y n c a io . c nd n q ibr m sso ia e it e e fe o me t in t e in o a io se t r w h d t r h n v t n c o , hic e e mine t e r t o e hn l g a o r ss a h tin a t s h a e ft c oo ic lpr g e tt a st n . 7 A n a t r t e a o c is t a l w f rd l e na iv ppr a h o lo o iminishing r t ns in a g e a e R &D butf rc nst n e ur in e ur g rg t o o a tr t ns t r se r h e o t o indiv ua e r pr ne s; in t c se no r st ic io a e ne e r o t numbe o he e a c ¤ r s f id l nt e e ur his a , e r t ns r c ssa y n he r f r se r he s o ho e a e in r se r h. T his a£ o c is pur d f re mpl , in St k y (19 9 5). U nde his e a c r rw ng g s e ac ppr a h ¤ sue , o xa e oe rt sc na io c nd io (1.3) be o is r pl c d by n ¡1 Á (n ) vt = 1. N o o t q l a iv pr d t ns o t e r , o it n lw e ae ne f he uait t e e ic io f he mo lw ul bec ng d In a dit n, f rt o a l st it unc io Á (n) = © n » St k yc nsid r Á 0(n ) is de o d ha e . d io o hec nst nte a ic yf t n oe o e s, pr po t na on ¡1 Á (n), in w h c se t c l a io e r ise o t o r io lt hic a he a ibr t n xe c n hesize o r w h e e t r po t d in Se t n fg o t ¤ c s e r e c io 3 w ul a sobe unc ng d o d l ha e . 10 T h r t a ao o t h Á t r in L u a is a eis n l g us ot e e m c s’spe i…c t n. c a io Thema st p in sov gf re u ibr m is t l ef re o me tin t ein o a io se t rn in e l in o q il iu osov o mpl y n h n v t n co . T od his, I ma euseo h sto de o d io ot k ft e…r r rc n it n(1.3), w hr l t s nt h aueo hic e a e ot ev l fapa e t tn v. T osov o , I e pr ss v in t r o t bt in a e u ibr m c n it n st ic l l ef rn x e e ms fn oo a n q il iu o d io r tyin t r e ms ofn. H e e I u t a o c o u a (19 7 8). T h tis, su se t is e o o h d ama k t r, se he ppr a h fL c s a ppo h c n my a re f rpa e t Sin e t e r pr se t t e a e tmusto n alpa e t in e u ibr m, t e v l e o o t n s. c h e e n a iv g n w l tn s q il iu h au f a pa e tmu tn stbe su h t a h a e tis in i¤ e e tbe w e bu ingo a d se l go e T h c h tt e g n d rn t en y ne n lin n . e e pe t d ut it fo bu in a pa e tis t e ma g a a u o o su x ce il y r m y g tn h r in lv l e fc n mpt n o c u d a o d io ne o l ¤ r w h t e pr …t ity l T h h s a e pe t d u il yv l eo it h o s ieds. is a n x c e t it a u f · 1 Z ¸ 0 dts C+ ¡½(t s) + Et U ( t s) C+ ¼ t se + ds 0 dts Y+ T h ha t is s obe t sa a t e u il y f o se l gt e pa e t In t a a , t e c n me a he me s h t it r m lin h tn . h tc se h o su rc n in r a h inc me by v, w ic a l w him t in r a c re tc n c e se is o h h lo s o c e se u r n o sumpt n T h a it na io . e dd io l u il yf o t o io is g e by t it r m his pt n iv n dt C U 0( t C ) vt dt Y Ind e e c i¤ r n ebe w e t e t oy l s t e v l fasu c ssf lin o a io : t e n h w ie d h aueo ce u n v t n · 1 Z ¸ U 0( t s)d t s=d t s C+ C+ Y+ ¡½(t s) + vt= E t ¼ t se + ds 0 U 0 Ct ( ) d t Yt C =d T h f lo in l mma e a ish s t t vt is w l-d …n d w e ° ¸ 1 , a d is l a e ol w g e st bl e ha el e e h n n ine rin pr …t o s u de h t or g s, ¼ 0 a d ¼ 1 . It pr o, a w l s t o o l t e l ims in t e pa r n rt e w e ime n s o f s ela h se falo h rca h pe , is d l g t d t h ppe d . e e a e ot eA n ix Lemma 1: Su se ° ¸ 1 . In a M a k v st t n r e u ibr m, t e v l e o a su c ssf l ppo r o a io a y q il iu h au f ce u in o a io is g e by n vt n iv n 8 1 > > !( 0 ) n )¡¹ 2 ( n ) 0 + ¹¼ 1) ifG t= G 0 > < n !( 1 !( 0 ¼ vt= (1.4) > > 1 > : ( n ) 1 + ¹¼ 0 ) ifG t= G 1 !( 1 ¼ !( 0 ) n )¡¹ 2 n !( 1 w ee hr !( )= ¹ + ½ + Á ( ) + ( ¡1 ) n¸] n n [1 ° l 11 Ifn0 = n , t ev l eo 1 h au fapa e tv ishig e tn h rinw h v rr g hic e e e imeo e shig e o s¼;in uit e y ¤ r h rpr …t t iv l , a pa e tis mo e v l a e ifitpa s o th h div e s t d y r t e ha in t e d o n e tn r au bl y u ig id nd o a a h rt n h isc u t d f t r. B u uue tifn 6 n , t epa e tc u dbemo ev l a ew e pr …t a er l t e yl w sinc 0 = 1 h tn o l r au bl h n o s r e a iv l o , e v de n s n to l o t e t pe d o n y n h imin fpa o s bu l n t e in o a io r t Á ( ) T h r t go y ut tasoo h n v t n a e n . is a e a e t t ev l eo ¤ c s h au fapa e tint od in tw y Fir , Á ( )r ‡e t t er t tw ic tn w ist c a s. st n e c s h a ea h hapa e ttn is r n r d o l t by t e a r a fa su r rt c n l g ; a hig e ( )t r f r r d e e de e bsoe e h r iv lo pe io e h oo y h rÁ n he e o e e uc s e pe t d f t r o s, ma ingt x c e u u epr …t k hepa e tl ss v l bl . Se o , Á ( )r ‡e t t r w h r t t n e aua e c nd n e c s heg o t a e o h v r l c n my w ic o l ft eo e a le o o , h hc u dma eapa e te h rmo eo e aua e W it k t n it e r rl ssv l bl . hmo er pid r a g o t in pr du t it , r a r wh o c iv y e linc me g o s mo e r pid y r isin e n f re c g o . T h o rw r a l , a gd ma d o a h o d is in r a s f t r x c e pr …t ma in c e se u u ee pe t d o s, k gpa e t mo ev l bl . O n t eo h rh n , t emo e t n s r aua e h te a d h r r pidl inc me g o s, t e mo e un v n is t a t ipa e f u e pr …l o o su a y o rw h r ee he n ic t d ut r o e fc n mpt n T h io . is ma e c r n o su k s ure tc n mpt n mo e v l a e r d c g t e v l e o h pa e t W hic o he io r a u bl , e u in h a u ft e t n . h ft se e e t d min t s d pe d o h wmu h t e c n me ¤ cs o a e e n s n o c h o su ris w l gt bst u e in e t mpo a l . ilin osu it t t re r ly W h n ° ¸1 , sot a e tis r l t e y l ss t l r n o a d u v n c n mpt n st e ms, t e e he g n e a iv l e oe a tt w r s ne e o su io r a h v l eo t n n mbig o sl e r a s w h Á ( .8 a u fapa e tu a u u yd c e se it n) T o e pr ss v soe y in t r o , I n e t e pr ss pr …t ¼ in t r o . H e e I u t e x e ll e ms fn ed o x e o s e ms fn r, se h f c ha g r g t pr …t ¦ r pr se tc a tt ta g e a e o s e e n umu a iv pr …t f o alse t r ne ft e c st o l t e o s r m l c o s to h o s f in o a io . T h tis, n vt n a Z1 Z1 ¦= ¼j j ¡ d n d = ¼ ¡n jj 0 0 Combin gt is e u t n w h (1.2) g e pr …t ¼ a af n t n o in h q a io it iv s o s s u c io fn, ¼ = ( ¡1 ) L ¡n¡N ) ¸ ( w ic a l w u t r w it (1.3) a a sy e o t o e u t n w h n0 a d n1 a t e o l h h lo s s o e r e s st m f w q a io s it n s h ny e do e us v r bl s: n g no a ia e ¸ ¡1 Á 0( i n) [( nj ¹) ¡!( j ( i+ N i !( )+ L n)n )¡¹ ( j+ N j ] 1 n )= (1.5) !( 1 ) n )¡¹ 2 n !( 0 W h e o a ing a co d f r sou io f r n a d n is n t g n r ly po il bt in l se o m l t n o 0 n 1 o e e al ssibl , I c n st l e a il c a a tr h r c e izeh we o me t g o t , pr …t pa e tv l e a d g o inc mev r c o t e o mpl y n , r w h o s, t n a u s, n r ss o a ya r ss h t or g s. w e ime 8 T hef c o v l s o o us n aue f°g e t rt n 1 is a sow r a e bye r a e ha l a r nt d mpir a vide eo t ic le nc n hein e mpo a l st it tr r le a ic y ofsubst ut n. Se , f re a e Epst in a Z inn (19 9 1). it io e o x mpl , e nd 12 P r po io 1: Su se ° ¸1 . T h n in e u ibr m, o sit n ppo e q il iu 1. Empl y n o me tin t e inn v t n se t ris in r a h o a io c o c e singin G , i.e n > n . H e c , t r w h . 1 0 n e heg o t r t ( ) n¸ is inc e sin a eÁ n l r a gin G . 2. T hev l eo t n s is in r a gin G , i.e v1 > v0 . au fpa e t c e sin . 3. N o a o s a ein r a gin G , i.e ¼ 1 > ¼ 0 . min lpr …t r c e sin . 4. N o a min linc me Y a d c nsu o n o mpt n P C c u d be e h rinc e sin rd c e sin io ol it e r a go e r a gin G ; h w v r bo h a e r l t d t o e e , t r ea e oG in t hesamew y a. P r po io impl st a o sit n1 ie h tashif ting v r me tspe d gt w r s g o c e e a e n v t n oen n n in o a d o dsa c l r t sin o a io , in r a s pr …t a r ise pa e tv l e In u iv l , ash tin g v r n c e se o s, nd a s t n a u s. t it e y if o e nme tspe d gt w r s n in o a d g o sin r a sd ma d, a dc n q e typr …t f re e yo r t gmo o l . W h npr …t o d c e se e n n o se u n l o s, o v r pe a in n poist e o s a eh he , t e eisg e t rin e t et a u et ema k t soninc e se T h a st eg o t r ig r h r r a e c n iv oc pt r h re, r a s. isr ise h r w h r t fl bo o u t it , w ic is e u lt ( ) n¸, a d w ic is a sot eg o t a eo e l a eo a rpr d c iv y h h q a oÁ n l n h h l h r w hr t fr a Y_ C_ o t t a ra o u pu nd e lc nsumpt n . io Y C T or l t r po io t e a eP o sit n1 omo ef mil rno io o r a ia t ns fbusin ss c ce itw lbeu f lt e u nt e y l s, il se u or t r o t eo ig a u a se u R e alt a epo s t er pr se t t ea e tr c iv s ac n h r in lL c s t p. c l h th sit h e e n a iv g n e e e o sumpt n io st e m o h o m r a ft ef r " t # Y C t= ( + Á s) ( + ") 0 1 1 tC s= 0 £ t Q ¤ w e e t r w h r t Á s is a me c n a t T het r h r heg o t a e ssu d o st n . em s= 0 ( + Á s) C 0 d n t s e pe t d 1 e oe x ce c n mpt n g e c o su io iv n umul t e g o t u t pe io t w il a t a o su a iv r w h p o r d , h e c u lc n mpt n di¤ e s fo io r rm t ise pe t t nbyast c a ict r 1 + " t a e c s c cic l‡u t a io s. A s a t ipa e h x c a io o h st e m t h tr ‡e t y l a cu t n n ic t dby my pr v u r ma k t is mo e d s a a a o o s c n in o ime r pr se t t n f rt e e io s e r s, h d la mit n n l g u o t u us-t e e n a io o h c n mpt n a g e a e o su io g r g t : · t Z ¸ C t= e p x Á ( s) n¸d ( + "( t ) 0 n l s 1 G )C (1.6 ) 0 Th v teo u e ir u f sing l bo a t n a r s he ume a e g o is t a no a q a t ie c re n t r ir o d h t min l u n it s o r spo d o d t e de e lq a t ie T h e r n dr a u n it s. isisbe a sea g e a er a a ia e r wa h mer t sl bo c u g r g t e lv r bl sg o tt esa a ea a r 13 pr d t it . Ex e h gt v l e o u n it s in t r o n s o a re e t e y r mo e o uc iv y pr ssin he a u fq a t ie i e ms fu it fl bo ¤ c iv l e v s Rt t eg o t t r e p 0 Á s l h r wh e m x n¸ in (1.6 sot a min lc n mpt n w lbe pr po t n lt ), h tno a o su io il o rio a o 1 + ". T hisal w st e o e e ia io sf o t e dc n mpt nusin o t lo su or c v rd v t n r m r n o su io gn mina o su lc n mpt n io , a d simil ryf ro h rr a n a l o t e e lma r e o o c o c n micse ie in t e mo e . rs h dl A r d w h t o r a io w a in e pr tP r po io 1 a ast t me ta u hec cic l me it his bse v t n, ec n t r e o sit n s a e n bo tt y l a pr pe t s o a io v r bl s in t e o o . Itis n t r lt …n hec cein t r o e l o r ie fv r us a ia e his c n my a u a ode et y l e ms fr a g o in o , i.e t e e o o is sa t r ss c me . h c n my id obe in abo m ifin o is a v it e pe t d g o t o c me bo e s x c e r w h r t . T his o c sw nn mina r ss in o ae c ur he o lg o c meY a me it ssu s shig e au . P r po io impl s h rv l e o sit n1 ie c n mpt nispr c cic l i.e ita t in sh h rv l ew e o o su io o y l a, . t a sit ig e a u h nn minalinc mea t in sh h r o t a sit ig e v l e M o e v r sinc h e u l ie au . ro e , et ein q a it sinP r po io a est ic , e o me tint ein o a io o sit n1 r r t mpl y n h n vt n se t r pr …t e u y v l e a g o t al ‡u t a e o e t , at o g t dir c io o c o , o s, q it a u s, nd r w h l c u t v r ime lh u h he e t n f t e se ie o e h c ce is a h se r s v rt e y l mbig o s. T he f c h tg o t c u d be e he o y l a r uu a tt a r w h o l it rpr c cic lo c u t r y l a sh u d n t be e t e y su pr o n e c cic l o l o n ir l r ising A g io a d Sa t P a l(19 9 8 ) pr v u y . h n n in u e io sl sh w dg o t o l o e r w hc u dbee h rpr c cic lo o n e c cic l d pe d go h it e o y l a rc u t r y l a , e n in nt espe i…c t nf r c a io o R &D . T h mo e is d lma e asimil rpr dic io bu o ks a e t n, tf radi¤ e e tr a n w h mo o l r n e so : it n poypo e wr in t e pr d c io o o d d e t g w r e s f o pr d t n t in v t n r d c s c r n h o u t n fg o s, iv rin o k r r m o uc io o no a io e u e ure t in o . Ift e in r a in G div r s e o g r so c s t in o a io , g o in o c u d f l c me h c e se e t n u h e ur e o n v t n r ss c me o l al e e se c o u e ’ pr …t ise T his is simil rt ¤ e tinH e pma n r j e be g(19 9 8) v na a hpr d c rs o sr . a oe c l na dT a t n r w e et ea r a famo epr du t et c noo yc u sin o h r h r iv lo r o c iv e h l g a se c met a la e ur e r of l sr so c sa ediv r e e td t in o a io . Empir al , pr …t e u y v l s, a d R &D e pe d ur s a e alpr c cic l o n vt n ic ly o s, q it aue n x n it e r l o y l a, w ic h hpo t t o y l a r w h T h is asopl usibl iv nt a n v t nr pr se t o l in s opr c cic lg o t . is l a eg e h tin o a io e e n s n y asmalsh r ft g r g t e o o . F r u a ey t o g , w e h rg o t is pr c cic lo l a eo hea g e a e c n my o t n t l , h u h h t e r w h oyl a r c u t r y l a ir e e a tf rho a iza io ¤ e t r w h T h a t rd pe so h t e o n e c cic lis r l v n o wst bil t na c sg o t . el t e e nd nw e h r Á ( )is c n a e in " no n w t rÁ ( )is in r a g o e r a gin " Itis t t is issu " o cv , to he he " c e sin rd c e sin . o h e t a n wt n. h tI o ur W h e itis u f e ist a l t e e n a iza io a f v r bl f rg o t w e e e h il se ulh ur ic ly or pr se tst bil t n s a o a e o r w h h n v rt e g o t r t is c n a eint el v lo c no r w h a eÁ o cv h e e fe o mica t it , r c l h tt eg o t a ea c iv y" e a lt a h r w hr t ndt e h l v lo c n mica t it r t r e e e fe o o c iv ya ede e min dsimu t n o sl l a e u yine u ibr m. H e e t ee u ibr m q il iu nc , h q il iu g o t r t is no t c nic ly a f c io o t e sc l o e o o r wh a e t e h al un t n f h ae f c n mic a t it . T o d t r e if c iv y e e min st bil t n in r a s l ng un g o t , t e , w a iza io c e se o -r r w h h n emu stin r du e ast bil t n poic d e ty to c a iza io l y ir c l in o t e mo la c mpa e it e u ibr m g o t r t w h t e g o t r t t a e a s t h de nd o r s q il iu r w h a e it h r w h a e h tpr v il w e ‡uc u t n a e al w d Sin e g v r me tspe din is t e so r e o hn t a io s r lo e . c oen n n g h u c f‡uc ua io a d t t ns, n 14 sin e it l v lis se c s ee tby poic ma e s, itse ms n t r lt d …ne a st bil t n poic a o e l y kr e au a o e a iza io ly s n w ic se s g v r n spe d g o g o s c n a t a t e a e a e o t t o r g s, i.e h h t o e nme t n in n o d o st n t h v r g f he w e ime . 1 G » G f ralt L e G t= ( 0 + G 1)= o l . tn( )d n t h umbe fw r e se o e G e o et en ro o k r mpl y dinin o a io n vt n 2 nd g o st n n q a o n ¤G w e g v r me t spe in is c n a t a d e u l t G , a d n ( )de o e t e n h n oen n n t h umbe o r f w r e s e o e in in o a io w e g v r me tspe d g ‡u t a e bu o k r mpl y d n v t n h n oen n n in c u t s tis c r e ty e ua u rn l q l t . St bil t n w lin r a v r g o -r g o t ifa d o l if oG a iza io il c e sea e a el ng un r w h n ny ¡ ¡ ¢¢ Á n G l > n¸ 1 2 [Á ( ¤( 0 ) l + Á ( ¤( 1) l n G ) n¸ n G ) n¸] (1.7 ) T h no a io is me n o sug e h tst bil g g v r n e tt n a tt g stt a a izin o e nme tspe din in t is e o o w l n g h c n my il in r a r w hift eg o t r t ( ¢ l is “e e t eyc n a e in g v r me tspe d g c e seg o t h r w h a eÁ n() n¸ ) ¤ c iv l o c v ” oen n n in o go n o ds. T his is a mo i…e n t n o o a it , sin e (1.7 ) c mpa e t e a e a e r a ize d d o io fc nc v y c o rs h v r g e l d g o t a eun e w i¤ e e tst c a icpr c sse o t i.e itc mpa e h u t nÁ ( ¢ r w hr t d rt od r n o h st o e sf rG , . o r st ef nc io n() ) a it h v r g fad e e tf nc io Á ( ¤(). T h r a o c v y o ()e a ish s tG w h t e a e a e o i¤ r n u t n n ¢ ) e e lc n a it fÁ ¢ st bl e t ef lo in h ol w gsu ie t(bu o e e r ) c n it n f rst bil t n t c e seg o t : ¢c n tn tn c ssa y o d io o a iza io oin r a r w h P r po io 2: (1.7 ) is sa is…e ifn is e e t e yc n a ein G , i.e if o sit n t d ¤ c iv l o c v . ¡ ¢ ¤ ¤ n G ¸ 1 [n ( 0 )+ n ( 1) 2 G G ] (1.8) Ino h rw r s, st bil t nin r a s g o t t e o d a iza io c e se r w hifitin r a s a e a ein e me tn Impo t n l , c e se v r g v st n . ra ty t o g , st bil t n in r a s g o t e e if(1.8 ) h l s w h e u l y i.e w e st bil t n h u h a iza io c e se r w h v n od it q a it , . h n a iza io h s n ¤ e to a e a e in e me t T his is be a se w h d a oe c n v r g v st n . cu it iminish g r t ns t n v t n in e ur oin o a io , t e f c h tst bil t n r d c s t e v l t it finn v t n a t it a t t c e se g o t . h a tt a a iza io e u e h oa il yo o a io c iv y c s oin r a r w h In u iv l , st bil t n sh t r so r e f o pe kpe io s o n v t n w e t e t it e y a iza io ifs e u c s r m a r d fin o a io , h n h irma g l r ina pr d tis l w t pe io s o e in e e in o a io , w e t e o uc o , o r d fl ss t nsiv n v t n h n h irma g lpr d tis h h r ina o uc ig . O fc u se t e r su t o r , h e l ingin r a in g o t c u d be o se c e se r wh o l ¤ tifst bil t n a sor du e a e a e a iza io l e c s v r g e o me tin t e in v t n se t r i.e ifc nd io (1.8 ) is v l t d T he mo e o s no mpl y n h no a io co, . o it n ioa e . d ld e t al wu t lo s opind w h t r(1.8) isinf c t d sin et is d pe d o h h dd r a iv o nw e he a tsa is…e , c h e n s nt et ir e iv t e o () T o se w y r c l ha is d t r e by t …r r e o dit n Á 0( v = 1 . In fÁ ¢. e h , e alt tn e e min d he sto d rc n io n) o d rt st bl r e oe a ishw e h rn d pe ds o inac n a eo o v xma e , w i¤ e e t t h hte e n nv o c v rc n e nn r ed r n ia et is …r r rc n it nt ic , w ic in ov s t et ir d r a iv 00 w o sto de o d io w e h h v l e h h d e iv t eÁ 0 h sesig n ma n u eis na d g it d ambig o s. T his a uu mbig it r ‡e t a in e e min c in t e r l t n u y e cs n d tr a y h ea io ship be w e in e me t t e n v st n a d u e t in y t a h s a r a y be n w l ppr c t d in t e l e a u e d pe d g o t e n nc r a t h t a l e d e e la e ia e h it r t r : e n in n h 15 pr d t nf n t na h v st n o u t n in e me tc ne h rin r a rd c e se o uc io u c io ndt ein e me tc stf nc io , v st n a it e c e seo e r a e n oame n pr se v gspr a in pr …t bil y9 in r spo se t a e r in ed o a it . T osumma ize st bil t nh s a mbig us e e to r w h tu e imin r , a iza io a na uo ¤ c ng o t ;bu nd rd ishin e u n gr t r s, st bil t nu a a iza io n mbig o sl c e se g o t o u u yin r a s r w hf rag e l v lo v r g iv n e e fa e a einv st nt T obe t r e me . te u de st n t oeo h a t rc a n l I f c s o t e spe ia a in w h st bil t n h s n r a d her l ft el t e h n e , o u n h c lc se hic a iza io a n ¤ e to t ea e a ein e me t i.e w e e n is e e t e yl e r oe c n h v r g v st n , . h r ¤ c iv l in a : ¡ ¢ ¤ ¤ n G = 1 [n ( 0 )+ n ( 1) 2 G G ] (1.9 ) A sid fo t e r t a t r st t e eis e e r m h o e ic lin e e , h r mpir a u i…c t n f rc n io (1.9 ) in t e r c n ic lj st a io o o dit n h ee t w r o a y a d R a y (19 9 5), w o k fR me n me host d t e r l t nsh be w e g o t a d v l t it u y h e a io ip t e n r w h n oa il y f rasa eo 2 c u t ie a d asu to o mpl f9 o n r s n bse f24 O ECD c u t ie T h y…n inc e se oa il y o n r s. e d r a dv l t it in o t t g o t is a c t d w h l w r a e a e o t u pu r w h sso ia e it o e v r g u put g o t , but n t w h sig r wh o it ni…c n at d e e c sinin e me tr t s. R a ya dR a y…n hispu in iv nc n e t n lw o i¤ r n e v st n a e me n me dt zzl gg e o v n io a isd m t a q a e g o t e e t w h c a g s in in e me t H o e e , t pa t r is c n e t h te u t s r w h ¤ c s it h n e v st n . w v r his t e n o sist n w h t en t nt a it h o io h titis dimin in e u n t no a io r t e h n c ng s in t e e f ish gr t r s oin v t n a h rt a ha e hel v lo in o a io t a e d st bil t n t ¤ e tg o t . T h s, t e n v t n h tl a a iza io oa c r w h u h ir…n in s su g stw c n ig o e d g ge e a nr c a g s in a e a e in e me tin st y gt e e t o a iza io o g o t .10 U n e h hne v r g v st n ud in he ¤ c s fst bil t n n r w h d rt is r st ic io , t e r t n hemo e n mbig o sl e ic sst bil t nin r a sg o t . M o eimpo t n l , d lu a u u ypr d t a iza io c e se r w h r ra ty t is in r a in g o t r ise t ew la eo h e e n a iv g n . h c e se r w h a s h e f r ft er pr se t t ea e t Th a el stst t me ta v nd r o e a a e n bo eu e sc r s nimpo t n bse v t n: e e ho hbo hd ra to r a io v nt ug t iminish g in r t r s a d c a g s in a e a e in e me tal w st bil t n t a e tl ng u g o t , t e eun n h n e v r g v st n lo a iza io o ¤ c o -r n r w h h t oc nn l ha ed e e timpl a io s f rw la e Ifst bil t nr ise g o t w ha e s v i¤ r n ic t n o e f r . a iza io a s r w hbyinc e sin ra g a e a e in e me t t e e t o w la e is a v r g v st n , he ¤ c n e f r mbig o s: sh t g r so r e f o pr d t n uu ifin e u c s r m o uc io in o in v t n c u d ma e t a e t be t r o o w r o , de n in o h pr f r nc s t no a io o l k he g n t e ¤ r o se ¤ pe d g n is e e e e be w e c r e t a d f u e c n mpt n. B u ifst bil t n in r a s g o t by r d c g t e n u r n n ut r o su io t a iza io c e se r w h e u in 9 Fo xa e H a t n(19 7 2) a re mpl , r ma ndA be l(19 8 3) d v l p mo e s w r e eo d l he einv st n e me tinc e se und runc r a t , ra s e e t in y w e B e na e (19 8 3) a D ix nd P ind c (19 9 4) d v l p mo e s w r in e me hil r nk nd ita yk e eo d l he e v st ntde r a s und runc r c e se e e- t in y Ca le o(19 9 1) pr se s a uni…e f a w r in w h inv st n a e he a t. ba l r e nt d r me o k hic e me tc n it rinc e se o e r a w h r a rd c e se it unc r a t , de ndingo t pa a t r o he pr duc io f t n a t in e me e t in y pe n he r me e s ft o t n unc io nd he v st ntc stf t n. o unc io 10 I sho d no e t tR a y a R a y use a br a me sur o v st nt w e inv st n ul t ha me nd me o d a e fin e me , hil e me tin t mo e his dl o yr ‡e t e nl e c s xpne ur s o R &D . O nesho dt r f r t r e heimpl a io o he e t f rt mo e dit e n ul he e o ein e pr tt ic t ns ft irr sul s o his dl w h so c ut n. St l t ne it me a io il, he xtse t n ilust a e a f c o c umul t n mo lw h simil rimpl a io a c io l r t s a t ra c a io de it a ic t ns nd w h a mit abr a e hic d s o d rint r e a io o v st nt e pr t t n fin e me . 16 t e v l t it o v st n , t g n il h oa il y fin e me t hea e tw lbe u a n mbig usl be t ro . T h f lo s f o t e uo y t e ¤ is ol w r m h w la e c l u a io s r po t d in L u a (19 8 7 ). R e alt a e …nd su a t lw la e g in ef r a c l t n e r e cs c l h th s bst n ia e f r a s f o in r a gt eg o t a eÁ w eh l inga e a ein ia o su r m c e sin h r w hr t hil od v r g it lc n mpt nC 0 …x d. T h e t io e en x l mma c n ms t t(1.9 ) insur s se t e o …r ha e t ingG t a s a e a e v l o tit v r g aue fG a sose s c n l t o sumpt n io e u lt s a e a e v l e q a oit v r g a u : Lemma 2: St bil g g v r me te pe it e o g o s asost bil s c n mpt n ifa d a izin o e n n x nd ur s n o d l a ize o su io n ol n yif(1.9 ) h l s, i.e od . ¡ ¢ ¡ ¢ P C G = 1 [P C ¤( 0 )+ P C ¤( 1 ) , 2 G G ] 2 ¤ G ¤ n G = 1 [n ( 0 )+ n ( 1) G ] D imin ing r t r s t e e o e c pt r t e in u io c n e e in Fig r 1, i.e st bil t n ish e u n h r f r a u e h t it n o v y d ue . a iza io r su t inac n e ls o sumpt nst e m t a r in t s a h mein ia e e io r a h to ig a e tt esa it ll v lbutg o s mo er pid y rw r a l t e e fe . B y c n r st ifst bil t n inc e se g o t by sh t gr so r e in oin o a io , h r at r o ta , a iza io r a s r wh ifin e u c s t n v t n t e r su t g c n mpt n st e m w u d st r t a l w r a e a e c n mpt n l v lt n is h e lin o su io r a o l a ta o e v r g o su io e e ha ilu r t dint eFig r . A nin r a l st a e h ue c e seing o t uet ig e v r g v st n il h r f r r w hd oh h ra e a ein e me tw lt e e o e n tg ne a e t sa w la e g in a asimil rin r a in g o t f o d o e r t he me ef r a s s a c e se r w h r m imin in e u n ish gr t r s, w ic h his a o h rr a n w yI f c s o h a t rc a ne. H e e ifst bil t na e tg o t n t e e so h o u nt el t e h n l nc , a iza io ¤ c r w h ol t og d n y hr u h imin in r t r s, t g o t e e t o ish g e u n he r w h ¤ c s fbu e c ce in ov un mbig o s sin ss y l s v l e a uu w la e c st T h k y q e io is w e he t se c st a e l r e t a t o c mpu e in ef r o s. e e u st n h t r he o s r a g r h n h se o td pr v u w r . T h a sw rt t q e io h g s o t o issu s. Fir , w n e t a ss e io s o k e n e o his u st n in e n w e st e e d o sse by h w muc bu e c ce r t r g o t f rpl u e d g e s o iminish g r t r s, a o h sin ss y l s e a d r w h o a sibl e r e fd in e u n n issueI a d e in Se t n 3. Se o , at o g d r ss c io c nd lh u h(1.9 ) r l s o tc a g s in a e a ein e me tby ue u h n e v r g v st n a mpt n w n e t ssu io , e e d oma e su e t a h n e in a e a e in e me td k r h tc a g s v r g v st n ono a e a it na th v dd io l impl a io s f rw la e t a ipe o tt e c st du t d ic t n o e f r h tw u h o s e o imin ishin r t r s. Jud in by t e g eun g g h e id n einR a ya dR a y t see e t r ik l obesmal Ina it n, t ene tse t n v ec me n me , he ¤ c sa el e yt l. dd io h x c io d v l ps amo e it i¤ e e tun e l inga mpt ns t tin r n h n e ine u ibr m e eo d lw hd r n d ry ssu io ha su ea yc a g s q il iu in e me t r g r l ss o he v st n , e a d e ft irimpa to g o t , in r a w la e In t is c se t e e t o c n r w h c e se ef r . h a , he ¤ c s f st bil t nh l a iza io odingt el v lo v st n e h e e fin e me t…x dne e r ypr v eal w rbo n nt ec st c ssa il o id o e u do h o s o sin ss c ce fbu e y l s. A sa…n lr ma k n t h tL e a e r , o et a mma2 impl sst bil ie a izingg v r me te pe d u e ng o l o e n n x n it r so o dsaso st bil s c n mpt n ifa d o l ifa e a e e o me tis u h n e . T h r ‡e t at me a ize o su io n ny v r g mpl y n nc a g d is e c s he t a a ot n be n ig o e in t l e a u e na l t t t r is n o e c r e tno io o h th s f e e n rd he it r t r , me y ha he e o n orc t n f 17 st bil t n. L uc s, f re a e c n e s a poic se t gc n mpt n t s a e a e v l e a iza io a o x mpl , o sid r l y t in o su io oit v r g au . T h mo e c n r a poic o se t g g v r n e pe d u e o g o s t it a e a e is d l o side s l y f t in o e nme t x n it r s n o d o s v r g v l e T h t o poic s a e o l e u a e tu e r n l a it c n it n a r pr se t d au . e w l ie r n y q iv l n nd rst o g ine r y o d io s, s e e n e by c n it n (1.9 ). W it ut l e r y it w u d be impo o d io ho in a it , ol ssibl t simu t n o sl se se e a e o la e u y t v r l ma r e o o c o c n micse ie q a ot e v r g . B u l ie ha a izedi¤ e e tma r e o mic r se u lt h ira e a e tpoic st tst bil rn c o c no v r bl s a ec n e ual u edi¤ e e t a d o a ia e r o c pt lyq it r n , n neh s t a obec r f a e ulin c mpa ingr su t ba d o r e ls se o di¤ e e tu e l in n t n o a iza io . T o t a nd impo n r n nd ry g o io s fst bil t n h te , sing (1.9 ) is t o e ic ly he r t al a ain ppe l gbe a set emo e o r spo d t x c l hesa cu h d lc r e n s oe a tyt meno io fst bil t nt a u a t no a iza io h tL c s u d in a g in se r u gbu e c ce in ov e a iv l sin ss y l s v l er l t e ymino o s. rc st 2. A l e n t e M o e s o n o e o s G r w h t r a iv d l fE d g n u o t A s n t d in t In r du t n v r u a t o s h v a r a y in e ig t d t e impl a io s o oe he t o c io , a io s u h r a e le d v st a e h ic t n f v l t it in mo e s o nd g n u g o t . H o e e , e e t o g t is l e a u e st d s t e oa il y d l fe o e o s r w h w v r v n h u h h it r t r u ie h e e t o a iza io o g o t ith s no ¤ c s fst bil t n n r w h, a tdisc d t e w la e impl a io s a c t d w h usse h e f r ic t n sso ia e it su hg o t ¤ e t n rh s ite a c r w he c s, o a x mine o he dh wt semo e s r l t oL u a e f r ac l t n d l e a et c s’w la ec l u a io s. T h se t n r v s t is l e a u e a d d u s it r l t n ip t h mo e ft e pr v u is c io e isit h it r t r n isc sse s e a io sh ot e d lo h e io s se t n. T h r a e t or a ns f rd ingt c io e e r w e so o o his. Fir , t e g o t e e t d sc ibe in pr v u st h r w h ¤ c s e r d e io s w r r ‡e tc a g s in a e a e in e me tr t rt a d ok e c h n e v r g v st n a he h n imin ishin r t r s. A s su h t se g eun c , he mo e s d o c ssa il impl f st rg o t is be …c lf rt e a e t M o e v r t y c n d l on tne e r y y a e r wh ne ia o h g n . r o e , he o - t ue t in oimpl o l ne l ibl c st o sin ss c ce f rr a n bl pa a t rv l e w ic y n y gig e o s fbu e y l s o e so a e r me e au s, h h h h ig t t eimpo t n eo imin ig l h s h r a c fd ishin e ur s. Se o d, pr v u a ho s h v eie nmo - gr t n cn e io s ut r a er l do d e s o a t ra c mu a io w h l e rpr d t n t c oo ie t e e a e e o e o s g o t l ff c o c u l t n it in a o uc io e hn l g s og n r t nd g n u r w h r t e h n t c n l g a n v t n T his se t n sho s t tt is di¤ e e c is ire e a t a d a h rt a e h oo ic lin o a io . c io w ha h rn e rlv n , n t er su t o h e io s se t nc u dbeo a dinmo l w e ef c o c u l t nis t e h e ls ft epr v u c io o l bt ine des h r a t ra c mu a io h e g e o r w h Sin e t e mo e i¤ e s in se e a ime sio s f o t e o e in t e pr v u n in fg o t . c h d ld r v r ld n n r m h n h e io s se t n, it ca i…e t a me o he simpl y g a mpt n in t e pr v us se t n a e no c io l r s h tso ft if in ssu io s h e io c io r t r spo sibl o s r su t e n ef rit e l s. Co side h f lo in mo l t k n f o Jo e M a u li, a d St c h t i (19 9 9 ).11 T ime is n rt e ol w g de, a e r m n s, n el n ac et 11 A sid r m Jo s, M a li, a ef o ne nue l ndSt c t i, v r us a ho s ha euse his mo lt ud ndo e us g o t a he t a io ut r v dt de ost ye g no r w h und runc r a t . Itw s …r e e o da e e t in y a std v l pe samo e fsa d lo vingund runc r a t e e t in ybyL e ha i a v r ndSr a n(19 6). iniv sa 9 T he sov a in…nit ho izo v r n o pr bl m …r y le n e r n e sio fa o e ststudie by P he ps (19 6 L e a (19 7 4) subse ue ty d l 2). l nd q nl r in e pr t d t ir mo e in t r o g o t a Ea o (19 8 1) d mo r t d ho t int o uc g v r e t r e e he dl e ms f r w h, nd t n e nst a e w o r d e o e nme t n 18 d r t . T h r a e n wt oa e t t e r pr se t t e a e ta t e g v r me t T h a e t isc e e e e r o w g n s: h e e n a iv g n nd h o e n n . e gn h s n a rr so r e bu e do e it nin ia mo n 0 o a a. H easoha a c ss a ol bo e u c s, tis n w dw ha it la u tK fc pit l l s ce t a l e rpr d t n t c n l g t a o v rs a u ito a a t 1 + ¸ un s o ut , o in a o uc io e h oo y h tc n e t n fc pit lin o it fo put w e e¸ > 0 . Ea h pe io , t ea e tu s alo is c pit lt o u eo t t H et e hr c r d h g n se l fh a a opr d c u pu . h nde id s c e h w mu h o h o t t t c nsu o c ft is u pu o o me a d ho mu h t l a e a c pit l f r t subse u n n w c o e v s a a o he qet pr d t n T h is in c n r stw h t e pr v us se t n w e e t a e tw s u a e t v o uc io . is o ta it h e io c io , h r he g n a n bl osa e h in o is c mef rf t ec n mpt n. P r du t n de e ia e a a l ft e c pit l sot eo l o u ur o su io o c io pr c t s w ya lo h a a, h ny c pit la a a ef rpr d c io a a v il bl o o u t ninpe io r dt+ 1 ist a h hw s se sid h tw ic a ta einpe io . T h g n r dt ea e t h s ac n e t n lCR R A u il y f n t n o e o su a o v n io a t it u c io v rc n mpt n in e c pe io a d d o t t e io a h r d, n isc un s h f t r tar t u u ea a e¯. Justa be o e I u o e nme tpoic s t eso r e o c u t n in t emo e , at o g a s f r, seg v r n l ya h u c f‡u t a io s h d l lh u h s pr v u u h r a epo t do t poic e io sa t o sh v in e u , l ysho k c sint isf a w r r h r me o ka eiso r ict e h oo y mo ph ot c n l g sh c s. T ha ok tis, o ec nr in e pr tt n a e t r e hemo e so ew r e h oo ysho k r e‡u t a io s d la n he et c n l g c sd iv cu t n a dt xpoic n a l yisa st ume tt a izea a stt e T or ma o sist n it hepr v u nin r n ost bil g in h m. e inc n e tw ht e io s se t n, I w lst k t he in e pr t t n o o k o ig a ingfo g v r n c io il ic ot t r e a io fsh c s r in t r m o e nme tpoic . Sinc ly e t e e is no l bo , g v r me tspe in is d v t d e t e y t pu c a g o t t T o …na e hr a r o en n nd g e o e n ir l o r h sin u pu . nc it e pe dit r s, t g v r me tt x s t e in o o he a e t soitt k s afa t n ¿ o h s x n u e he o e n n a e h c me ft g n , ae r c io ft e o t tpr du e A s be o e t e bu g tis baa c d e e y pe io , i.e G t = ¿t t In c n r st u pu o c d. f r, h de ln e vr r d . Y. o ta t h pr v u se t n, G t n wd n t s r a o e n n ot e e io s c io o e o e e lg v r me tspe ing O n e a a , t sh r o nd . c g in he a e f g v r me tspe in a a me o l t ov l e w h I a me is i.i.d. o e ime 12 F o oen n nd gc n ssu n y w au s, hic ssu v rt . rm bu e l n e t is impl s t et xr t t c nt k nt ov l e ¿1 < ¿0 , e c q a l ik l . dg tbaa c , h ie h a a e¿ a a eo w a u s a he u lyl e y T h l a e t ea e tw h ( ¡¿t ( + ¸) t´( + ¸t Kt u s o u pu a hpe io .13 T h is e v s h g n it 1 )1 K 1 ) nit fo t te c r d e pr bl m f c o e a ingt e a e tis g e by h gn iv n " 1 # X C 1¡°¡1 t t ma E 0 x ¯ Ct t 0 = 1 ¡° su e tt bj c o Kt 1 = ( + ¸t Kt¡C t + 1 ) poic in ot f a w r . l y t his r me o k 12 B yc n r st t o t a , hepr v us se t n a e io c io ssume G t w s P o n, impl ingpe sist ntsho k Jo s, M a ue l a d a isso y r e c s. ne n li, nd St c he t (19 9 9 ) a soe a a c ti l x mine av r n o he mo e it pe sist ntsho k e sio ft d lw h r e c s. 13 1¡° I r st ic 0 a ¿1 sot t¯E [(1 ¡ ¿t + ¸)] e r t¿ nd ha )(1 < 1, w h insur s a in e io l io hic e n t r rsout n. 19 w e e K0 is g e a d 0 · C t · ( + ¸t Kt A ppl in a pe t r t n a g me tt t e …r hr iv n n 1 ) . y g ru ba io r u n o h st o d rc n it n o h g n , itc n besh w t tt e sou io t h pr bl m is g e by r e o d io s ft ea e t a o n ha h l t n ot is o e iv n C t = c( + ¸t Kt 1 ) Kt 1 = i( + ¸t Kt + 1 ) w e ei a d ca ec n a t i is g e by hr n r o st n s, iv n ³ h i´1 1¡° ° i = ¯E ( + ¸) 1 (2.1) a d c= 1 ¡i. T h g o t r t fc n mpt n is g e by n e r w h a eo o su io iv n ¢ Ct 1 + = i( + ¸ t 1 )¡1 1 + (2.2) Ct w ic in e u ibr m is asot e g o t r t o u pu . T heg o t r t pr po t n lt h h h q il iu l h r w h a e fo t t r w h a eis o r io a ot e in e me tr t i, a d t u de nd o t ebe a io ft ea e t v st n a e n h s pe s n h h v ro h g n . Justa in t s hepr v u se t n, w a g u et ¤ e t o a iza io byse t e io s c io ec n a g hee c s fst bil t n t ingt esh r f h a eo g v r me tspe din n o t t a d t u t e t x r t ¿, t s e pe t d v l . T h a u t oen n n go u pu , n h s h a a e oit x c e aue is mo n s t t in te u lt s a e a ev l . T h nl a h w la e tt v r g r w hr t ose t g¸ q a oit v r g aue eo yw yt is il ¤ c hea e a eg o t a ein (2.2) is bya e t gt epr pe yt v ¤ c in h o nsit osa ei. F o (2.1), st bil t nin r a s a e a eg o t rm a iza io c e se v r g r w h ifa d o l if° < 1 . Sin e e ima e o a e 1 o r a e , st bil t n e h rh s n ¤ e to n ny c st t s f° r rg e t r a iza io it e a oe c n g o t o a se itt a l in c n r stw h t r w h rc u s of l, o ta it hepr v u mo e . B u h a tt a a iza io e io s dl tt ef c h tst bil t n d c e se g o t d e n timpl h a e tis w r ¤ . A f e l, st bil t n in uc s al w r e r a s r wh o s o yt e g n o seo t ral a iza io d e oe g o t r t c u itl a s t ea e tc o se t ou t r y c nsu r w h a ebe a se e d h g n h o s ov l n a il o meag e t rf a t n o is r a e r c io fh o t t i.e t c e seca u pu , . oin r a ndr du ei = 1 ¡c R e e l dpr f r nc e c . v ae e e e eimpl s t a h g n ie h tt ea e tmust be be t ro u de o e r w h M o e g n r ly be a se t e e u ibr m in t is e o o is t e ¤ n rl w rg o t . r e e a l , c u h q il iu h c n my P a e oo ima , a yc a g r t pt l n h n ein t q ibr m l v lo v st n hee uil iu e e fin e me tmustma e t g n k hea e tbe t r te o , sin et ec n r lpl n e a o ¤ c h e t a a n rc nn tma et g n t e ¤ byr a l c t k hea e tbe t ro e lo a ingr so c s in oo e ur e t r o to h inn v t n se t r B y c mpa iso t e u ibr m in t e pr v u se t n w s no u ft e o a io c o . o r n, he q il iu h e io s c io a t P a e oo ima iv nmo poyd o t n a r t pt lg e no l ist rio s ndt ein bil yo g n s t h a it fa e t obo r wo e d, w ic ro rl n h h is w y c a g s in a e a e in e me tc u d h v r d c d w la ein t a r me o k h hne v r g v st n o l a e e u e ef r h tfa w r . Sin est bil t nc na e tt esa ing d c n o h g n , t is mo lasosu g st g o t c a iza io a ¤ c h v s e isio s ft ea e t h de l g e s r wh e e t w ic impl t a uc s’c l ul t n u d r st t s t w la e u d rst bil t n. In ¤ cs h h y h tL a ac a io n e e ima e he e f r n e a iza io t r o Fig e 1, t e w la e o t e h u hod a t r st bil t n d e n t c r e nd t e ms f ur h e f r f h o se l fe a iza io o s o o r spo o 20 t e c nsu h o mpt n pa h se o t e t e d r t o h o ig a o su io t tt h r n a e ft e r in lc n mpt n st e m; in e d t e io r a st a , h c n mpt n st e m u de a iza io c u d r t t d pe d g t h o imizin d c n o o su io r a n rst bil t n o l o a e e n in ot e pt g e isio f t e a e t B u he n wc nsu h gn. tt e o mpt n st e m u d rst bil t n w ln tbe t e sa a t e io r a n e a iza io il o h me s h d sh dl einFig r a e in u e1;f rt o mpt nst e m t v o hec nsu io r a oha east e rpr …l , i mustbeh h r e pe o e ig e . B u h impl s t a hein ia e e fc n mpt n C 0 = c 0 is l w r sin ec= 1 ¡i. T h s, tt is ie h tt it ll v lo o su io K o e, c u t e mo la v g n r t s a a d io a o fbu e c ce t a e c s t e e e t o h h de bo e e e a e n d it n lc sto sin ss y l s h tr ‡e t h ¤ c s ft e c ceo h imepr …l fc n y l nt et o eo o sumpt n bu h hr l s o h n e ina e a ein e me ta d io , tw ic eie nc a g s v r g v st n n is t e e o e d e e tfo t e c a n lo h r f r i¤ r n r m h h n e fdimin ingr t ns o tin d in t e pr v u se t n ish e ur u l e h e io s c io . M o e v r t mo e r o e , he d lsug e s t is e e tis l e y t g st h ¤ c ik l obe q it smalf rr a n bl e ima e o u e l o e so a e st t s f ° . F rt c se w e e ° = 1 , t e e a e n g o t e e t a d t e mo e e c s t t e o e o he a hr h r r o r wh ¤ cs n h d lr du e o h n c n e e in O bste d (19 9 4a w ic in ov s a w la e g in fo st bil t n o n y 0 : o sid r d fl ), h h v l e e f r a r m a iza io fo l 3%. U sin h st t dv l t it gt ee ima e oa il ying o t e re r w hr po t dint en x c io , I asoc mput dt ee e t h e tse t n l o e h ¤ cs o a iza io f rt a fst bil t n o hec sew e e° = 2. F rt is v l e t ea e a eg o t r t cine fo hr o h au , h v r g r w h a ede l s r m 2: 0 % t : 0 o1 98%. T h impl d w la e g in a e o e a a amo e ie e f r a s r nc g in l stide t a ot se r po t d n ic lt ho e r e byO bste d w ic sy e t al alw l o to %. f l , h h st ma ic lyf l e lsh r f1 W h e t e a v d ussio su g st e ist gmo e s o n o e o s g o t u e n e t in y il h bo e isc n g e s x in d l fe d g n u r w h nd ru c ra t impl o l smal c st o bu ss c ce w c u d e sil in r d c dimin ing r t r s in y ny l o s f sine y l s, e o l a y t o u e ish eun in e me tin ot semo e sa e o e h v st n t he d l ndr c v rt epo e t lf rmu hl r e ¤ e t F lo in za a t n ia o c a g re c s. ol w gU w (19 6), su set a h c pit lst c 9 ppo h tt e a a o kin pe io t+ 1 is g e by r d iv n Kt 1 = ©( t t + I ) ;K w e e I = ( + ¸ t Kt ¡ C t is t e pa t o d hr t 1 ) h r f ispo bl in o t a is no c nsume . T h sa e c me h t t o d e f n t n©(;¢ inc e sin n o c v u c io ¢)is r a ga dc n a einI T h f n t na o m impl s t a nl . is u c io lf r ie h to y©pe c n re t o v st n c u ly t ns in oc pit l w e t e ind ro v st n e t n u in t e fin e me ta t a l ur t a a, hil her ma e fin e me tis a e p h pr c ss o st lin t c pit l I f t e ssu t e in al t n f nc io e h s c n a t o e fin al g he a a. urh ra me h st la io u t n x ibit o st n r t r s t ae so e u n osc l , µ ¶ I ©( t t Á I )= ;K Kt K T h r w h r t o h c pit lst c o it na n da et is g e by eg o t a e ft e a a o kc nd io lo t iv n µ ¶ ¢ Kt It = Á ¡1 Kt Kt ´ Á [ i¤( t ( + ¸ t ] ¸ )1 ) ¡1 21 w e e i¤()is t e f a t n o fe -t x in o d v t d t in e me tw e ¸ ‡uc ua e o e hr ¢ h r c io fa t r a c me e o e o v st n h n t ts v r t . T h g o t r t is n tt e sa a t e c n io lg o t r t o o sumpt n bu ime is r w h a e o h me s h o dit na r w h a e fc n io , t t et og o t a e ha et h w r w hr t s v hesameu c n io a x c a io , a n o dit n le pe t t n nditis t e pe t t nw ic his x c a io h h is r l v n o e f r . St bil g¸ t c n in s t a e a e e a tf rw la e a izin o t ue oh v mbig o s e e t o e pe t d g o t u u ¤ cs n x ce r wh w ic d pe d o ° a d t e t ir de iv t e Á 00 H o e e , j h h e n n n h h d r a iv 0. w v r usta be o e dimin ingr t r s s f r, ish eun impl h tst bil t n w lin r a v r g r w h f rag e r t fin e me tt a a. yt a a iza io il c e sea e a eg o t o iv n a ioo v st n oc pit l W ec n isoa et e e e t o a l t h ¤ c s fdimin ingr t ns byr st ic inga t n io t h a ish e ur e rt t e t n ot ec sew e e t e hr h in e me tt a a a iois e e t e yl e r i.e w e e v st n oc pit lr t ¤ c iv l in a , . h r ¡ ¢¡ ¢ 1 i ¸ 1 + ¸ = [i¤( 0 ) 1 + ¸ 0 )+ i¤( 1 ) 1 + ¸1 ) ¸ ( ¸ ( ] 2 T h impl a io s w u d t e be id n ic la t o o he mo e e n e in Se t n 2. T h e ic t n o l h n e t a s h se ft d lpr se t d c io e o l i¤ e e c t a n yd r n eis h tun ik h tmo e , c a g s in a e a ein e me tr g r e o ir c io l et a dl hne v r g v st n e a dl ss fd e t n w ln c ssa il ma et e a e tbe t ro . T h s, t ew la e g in f o d il e e r y k h g n te ¤ u h e f r a s r m imin in e u n in ish gr t r s t is mo e e e n l w rbo n o t e c st o h d lr pr se ta o e u d n h o s fbusin ss c ce a itw lbe e o g t e y l s, nd il nuh o sh wd o iminish gr t r s o t e w g ne a e l r ew la e e e t t st bl t tbu e in e u n n h iro n e r t a g e f r ¤ c s oe a ish ha sin ss c ce a ec sty y l s r o l. 3 Q u n it t e A n l s . a t a iv ay is T h pr c d g disc e e e in ussio ha a g e t a n s r u d h tbu e c ce in ov w la e l sse t a pe a e sin ss y l s v l e e f r o s h to r t t r ug n g no r w hc a n l pa t u a l c u fd h o he do e usg o t h n e s, ric l rybe a seo imin in e u n ish gr t r sinin e me t v st n . Bu h tt emostin e e in ue io il e ins: a et seg o t ¤ e t a g n u ht e e a e t r st gq st nst lr ma r he r w he c sl r ee o g og n r t c st o bu e c ce t a e c e t o ba d o y o c n mpt n v l t it ? O n w y o s f sin ss y l s h t x e d h se se nl n o su io oa il y e a o a r ssing t q e io is t a r c f o t e so r e o d f dd e his u st n o bst a t r m h u c f iminishin r t r s a d f c s g eun n ou in e d o t r d c d f r impl a io s o h mo e o h r l t nsh be w e v l t it st a n he e u e o m ic t n ft e d lf rt e e a io ip t e n oa il y a d a e a e g o t . T h a o c o l r q ir s in o ma io o t e r l t n ip be w e n v r g r wh is ppr a h n y e u e f r t n n h e a io sh t en v l t it n g o t , e h ro e imeo r m ac o se t n o o n r s. Su h e ima e a e oa il ya d r w h it e v rt rf o r ss c io fc u t ie c st t s r r a il a a a e f o t e w r o a y a d R a y (19 9 5). U sin c o o n r e ide c , e d y v il bl r m h o k fR me n me g r ss-c u t y v n e te h y…n h tc n r lin o h v r g v st n dt a o t ol gf rt ea e a ein e me tsha e ao epe c n a epo tr d c io r, n re t g in e u t nin t e st n r d v t n o u pu r w h is a c t d w h a in r a d g o t r t o : h a da d e ia io fo t tg o t sso ia e it n c e se r w h a e f0 2%. Sin e t e st nd r de ia io o u putg o t in t e U .S. is 2: c h a a d v t n fo t r wh h 5%, t is impl s st bil t n h ie a iza io sh u d inc e se t e g o t r t fo 2: % t 2: ol ra h r wh a e r m 0 o 5%. A ppl in L u a st t t a n a e t y g c s’e ima e h ta g n w ul sa r e 20 % o o mpt n f ra 1 po t in r a in g o t w n ° = 1 impl s a o d c i…c fc nsu io o in c e se r w h he ie w la eg ino 0 % o it lc nsu ef r a f1 fin ia o mpt n t oo d r fma n u eg e t rt nL u a r ina io , w r e so g it d r a e ha c s’o ig l 22 e ima e M o e v r sin eR a ya dR a y…n oe ide c fsy e t h n e ina e a e st t . ro e , c me n me dn v n eo st ma icc a g s v rg in e me tr t sa c t dw hd e e tl v l fv l t it , t e esh u dben ¤ se t ge e t v st n a e sso ia e it i¤ r n e e so oa il y h r o l oo t in ¤ c s f o c ng s in a e a e in e me tt a o l l w rw la ein ase o d-be r m ha e v r g v st n h tc u d o e ef r cn stw rd ol . W h et e st t s impl n e o mo s c sto il h see ima e ya n r u o fbusine c ce w o l o e dw hso ss y l s, esh u dpr c e it me c u io be o e w a c ptt e a e ide c o o l bu ss c ce A fe l, d e e c s in a t n f r e c e h m s v n e fc sty sine y l s. t ral i¤ r n e g o t r t s a r ss c u t ie c u d be du t u me su e h t r g n it , a po r wh a e c o o n r s o l e o n a rd e e o e e y ssibil y t a it h tis u de sc r d byt ef c ha me o a ya R a y s e ima e c a g r ma ic lyw h n r oe h a tt tso fR me nd me ’ st t s h n ed a t al it t e a d io o e t in e pl n t r v r bl s. W h e t e h d it n fc r a x a a o y a ia e il h irpo te ima e f rt o ¢c n n in st t o hec e ie to v l t it t n s t oa il y e d obe cu e e a o n 0 : l st r d r u d 2%, t e st t s r ng be w e 0 : a 0 : h ire ima e a e t e n 1 nd 9%. In a d io , a t ug t n g t e r l t nsh be w e t e v l t it o r w h a t e a e a e d it n lho h he e a iv e a io ip t e n h oa il y fg o t nd h v r g r t fg o t st t ic lysig i…c n , itis no st t dw h g e tpr c n. T h su g st a eo r w his a ist al n at te ima e it r a e isio is g e s l o in o k gmo e d e y a h so r e o r e pl tt e u c fdiminishingr t r s t sse w e h ritc ul pl usibl e u n oa ss h t e o d a y g n r t n in r a e e a ea c e sein g o t f o 2: % t 5%. r wh r m 0 o2: F rst bil t n t g ne a e h h rg o t fo a g e l v lo n v t n t o c n it n o a iza io o e r t ig e r w h r m iv n e e fin o a io , w o d io s a e n c ssa y t e a u to no a io n h s t r e e r : h mo n fin v t n a obe v l t e o e h c ce a t e f nc io oa il v rt e y l , nd h u t n Á ( ha n)t tma r so r e e o e in in o a io in o g o t h s t be c n a e St n a d ps e u c s mpl y d n v t n t r wh a o o cv. a d r me su e o R &D in t c mpil d by t e N a io l Sc nc F un a io , in l ding in ust y a rs f pu s o e h t na ie e o d t n cu d r e pe d u e o &D a x n it r s nR ndt en mbe fw r e s e o e a sc n ist o n in e s, c r a l h u ro o k r mpl y d s ie t s re g e r e t in y eh x ibitv l t it o e ime o h n e in bo h se ie ha e ast nd r de ia io o bo t5%. oa il y v rt ;l gc a g s t rs v a a d v t n fa u M o e v r w r by F t s (19 9 4) sho s t a ha e in R &D e pe d u e a e r l t d t t e ro e , ok aa w h tc ng s x n it r s r ea e o h bu e c ce a t o g t t r l t n ip se ms t h v w a e e in t e 19 9 0s. B ut t se sin ss y l , lh u h ha e a io sh e o a e e kn d h he me su e ma a oa e u t l a u et oa il yinalo heinpu s t a n e t &D . a r s yf ilt d q a e yc pt r hev l t it l ft t h te t rin oR F re a e v l t it o x mpl , oa il yininn v t nmig tbebe t rr ‡e t dint imespe tbysc n ist n o a io h te e c e het n ie t sa d e g e r o no a io pr j c s r t e ha in e o me tn mbe s. T h is pa tya dr sse n in e s nin v t n o e t a h rt n mpl y n u r is rl d e d byusingR &D e pe it r s, bu his me su et ois l e yt x nd u e tt a r o ik l obepr bl ma ic F rin a c , t e o e t . o st n e h ph sic limpl me t t n o e e h l g s is l e y t y a e n a io fn wt c noo ie ik l obe c u t d a in e me tr t e h n o n e s v st n a h rt a R &D , e e t o g r so r e d v t d t v n h u h e u c s e o e oimpl me t t n sh u d be c u t d a in s in ot e e n a io ol o n e s put t h in o a io pr c ss. H e e in e d o aibr t gt e mo lt h v l t it o a ao R &D n vt n oe nc , st a fc l a in h de ot e oa il y fd t n e pe d u e I c l a eitt h oa il yo o su x n it r s, aibr t ot ev l t it fc n mpt ng o t . Ino h rw r s, r t e h n io r w h t e o d a h rt a ma c in t e v l t it o pu s t a o in o pr d ingin v t n I ma c t e v l t it o t h g h oa il y fin t h tg t o uc no a io , t h h oa il y f t eo t t o n v t n Sin e t h u pu s fin o a io . c heu t t g a t e ic h r w h r t lima e o lis opr d tt eg o t a ein t ea nc h bse e o y l s, itse ms o l r a n bl t c l a e t e f n t n Á ( )t t e g o t r t s w d fc ce e n y e so a e o aibr t h u c io n o h r wh a e e o 23 o r eo e h bu e c ce bse v v rt e sin ss y l . T o me sur v l t it in g o t in a w y t a is c n e t w h t e t e r t a r me o k a e oa il y r wh a ht o sist n it h h o e ic lf a w r a v , I d rt bo e isc e ize(1.6 a de ima eit d ry ) n st t sun e l ingpa a t r r m a u lc n r me e sf o nn a o sumpt nd t . io a a Themo limpl s c n mpt n be w e pe io t¡1 a t w lc ng f rt or a n Fir , de ie o su io t en r d nd il ha e o w e so s. st t c n l g a n v t n impr v s pr d c iv ya d al w mo ec n mpt n g o s t e h oo ic lin o a io o e o u t it n lo s r o su io o d obepr - o d c df o ag e mo n fr so r e T h g o t a eis e u lt ( t l u e r m iv na u to e u c s. is r w hr t q a oÁ n ) n¸, w hde n s hic pe d o h n ry gg o t e imeint ec r e tpe io . Se o d, r g nt eu de l in r w hr g h u r n r d c n e imec a g s t ig e h n e h n e r g rc a g s in t a u to e ur e e o e in pr d c io a d t u t l v lo o su he mo n fr so c s mpl y d o u t n n h s he e e fc n mpt n T h io . e cag h n ein l gc nsu o o mpt n be w e t ope io s is t r f r g e by io t en w r d he e o e iv n ¢ l t= Á ( t l + ( t¡"¡1 ) nC n ) n¸ " t (3.1) In…t in h o h st t gt isst c a icpr c sst c u lc nsumpt nd t , I ma t int o e oa t a o io a a in a heimpl ita ic ssumpt n io o w e ime w ic I d n t by st 2 f ;1 g.14 W it o tl ss o e r l y I d sig a e st = 0 ft or g s, h h e o e 0 h u o fg ne ait , e nt a t e l wpr d c iv y g o t r g , i.e Á 0 · Á 1 . L e s h o o u t it r w h e ime . t"= " ¡" de o e t e d e e c in 1 0 n t h i¤ r n e t e l v lo o mpt n a r ss t e t or g s. W it t is n t t n w c n r w it (3.1) a h e e fc nsu io c o h w e ime h h o a io , e a e r e s Á 0 ( ¡st + Á 1 st+ "( t¡st ) I t e st t 0 , Á 1, a d"f o a n a t 1 ) s ¡1 . h ne ima eÁ n r m n u lda abyminimizing t eme n sq r ro v ra lpo h a ua ee r ro e l ssibl q n e f t ese ue c s s g: 19 98 X 2 min ( l t¡[¸0 ( ¡st ¸1 st+ "( t¡st )) ¢ nC 1 )+ s ¡1 ] (3.2) sg Á 0 ;Á 1 ;";f t t 19 5 = 1 W ec n t inko his min a h ft imiza io pr bl m in t ost g s. Fir , f re c se u n ef t I l o t n o e w ae st o a h q e c s g, o k f rt e v c o Á 0 ;Á 1;" h h min o h e t r( )w ic imize me n sq a e e r r I t n l o f rt se u n e o s a u r ro . he o k o he q e c f r aiza io s st f rw ic t is min m me n sq a e e r ris l w st T hepr bl m w h sov g el t n o h h h imu a u r ro oe . o e it l in (3.2) is t a he n h tt ro ssibl se u n e in ov s 24 9 = 5: £1 0 14 c mbin t n T og t umbe fpo e q e cs v le 6 o a io s. e a h minimu I f lo a r u in t t is simil rt simu a e a n ain . T h tis, I g e tt e m, ol w o t e ha a o l td n e l g a u ss a in ia q e c o t a d t n a l wf rsma lst c a icpe t r t n a o n t e o ig l n it lse u n e fs n he lo o l o h st r u ba io s r u d h r ina se u n e Ifal w rv l eisa hie e I uset e q e c. o e au c v d, hen wminimum asmyinit lse u n e I r pe t d ia q e c . e a e t is pr c du efo se e a h o e r r m v r ldi¤ e e tin ia o d io s a r n it lc n it n ndasoal w df rl r e r u ba io s l lo e o a g rpe t r t n t he ka a stl c lo ima T h e ima e a h min m w r Á 0 = : 0 2, Á 1 = : 38, a d oc c g in o a pt . e st t s tt e imu ee 0 0 n 14 M a t iningt M a k v st uc ur is e nt lf ride t a io T o se w y c nsid rt g ne a q t n in a he ro r t e sse ia o n i…c t n. e h, o e he e r le ua io ¢ l C t = Á t+ ¢ "t T he pr bl m is t tsinc inno a io de nd o t sc l o c no n . o e ha e v t n pe s n he a e fe o mica t it , Á ("t a c iv y ) nd ¢ "t a ec r e a e . Ifw lo t t ol wag ne a ize A R pr c ss, itw lbeimpo r orl td ea l w" of lo e rl d oe il ssibl oide t yÁ ("t f o et n if ) rm ¢ "t sinc , ebo h r d et a unc io o t Ev n ifw t e uc ol gf t ns f" . e eimpo t t"t is i.i.d., w o d no pa a e yid n if se ha ec ul tse r t l e t y ½ (Á t "t a v r t H o e e , w a st le ima e ar ng f rv r t byl o inga r ss a lv l s o ;¢ ) nd a (Á ). w v r ec n il st t a e o a (Á ) ok c o l a ue f½. T he st nd r de ia io o t l s be w e 0 : a 3 0 % , w h incud s my e ima e o 8% be o . a a d v t n fÁ ie t e n 6 nd : hic l e st t f1: lw 24 "= ¡ 0 0 7 T his impl s t a h r w hr t : . ie h tt eg o t a ein c nsu o mpt nbe a seo e h l g a o r ss io c u ft c noo ic lpr g e ‡u t t s be w e 0 : a d 3: pe e r f ra a e a eo c ua e t e n 2% n 8% ry a , o n v r g f2% pe e r j sta L u a …n s. ry a , u s c s d T h a tt tt epo te ima ef r"isn g t esu g st o su ef c ha h in st t o e a iv g e sc n mpt ng o t io r w hisc un e c cic l o t r y l a, i.e c n . o sumpt n g o s mo er pid yifitis beo s e pe t d l v l T h …n io r w r a l l wit x c e e e. is dingis so w t me ha d ur ist bing sin e I pr v u y a g e pr c cic lg o t is mo e c n e tw h t e e , c e io sl r u d o y l a r w h r o sist n it h mpir a ic l e id n eo o y l a o s a v e c npr c cic lpr …t nde u yv l e H o e e , t isis n timpo t n o ac l t g q it a u s. w v r h o ra tf rc l u a in t ee e t o a iza io , a d a I d u f rhe l w itis no e yr bu . h ¤ c s fst bil t n n , s isc ss u t rbe o , tv r o st T h …n lst p in c mpu ing t e g o t e e t a c t d w h st bil t n is t spe if a e a e o t h r w h ¤ c s sso ia e it a iza io o cy n in o a io r t Á ( )a c l a e it so t a it g n r t s g o t r t s o 0 : n v t n a e n nd aibr t ht e e a e r w h a e f 2% a d 3: n 8%. P r v u mo e s o e hn l g a o r ss t a lo f rd e io s d l ft c oo ic lpr g e h ta l w o iminish g r t r h v t n d t in e u ns a e e de o » f c s o t c n a t ea ic y f n t n Á ( o u n he o st n l st it u c io n)= ©n ; f re a e t is is t spe i…c t n o x mpl , h he c a io St k y (19 9 5) u s t st d t impl a io s f rd oe se o u y he ic t n o imin in r t r s o e u ibr ish g e u n n q il ium g o t . r wh Thema d a t g ft eCES f n t nis t a ina v n a eo h u c io h titc r e nd t h u c io a o m e o r spo s ot ef n t n lf r mpir a ic l r se r h r h v e ima e f o mic o d t . In pa t u a , t e e is n w a siza e l e a u e e a c e s a e st t d r m r aa ric l r h r o bl it r t r t a st t s pr d c io u t n f rne h te ima e o u t nf nc io s o wid a byusin &D e pe it r s a t es gR x nd u e s heinputa d n pa e t a o t t T h spe i…c t na c r s w h ana r win e pr t t n o t n s s u pu . is c a io c o d it ro t r e a io finn v t nin t e o a io h mo e , sinc t e mo e r a s e c pa e ta a su c ssf lin v t n. M o e g n r ly n tal dl e h d lt e t a h t n s c e u no a io r e e al , o l pa e t c n r t e u ly t g o t bu st t s o imin in r t r s fo pa e td t t n s o t ibu e q a l o r w h; te ima e fd ish g e u n r m t n a a sh u dpr v ea ppe u do het u a l n s t o l o id nu rbo n nt r e» s o ga hepr du t no c e u n v t n o c io fsu c ssf lin o a io s eh sd x ibit imin in r t r s in t e n ish g e u n h umbe fpa e t G r ic e a P a e (19 84) a d H a l ro t n s. il h s nd k s n l, G r ic s, a d H a sma (19 86 bo h e ima e t t t ea ic y o il he n u n ) t st t ha he l st it fpa e t w h r spe t t t n s it e c o t t lR &D e pe dit r s a t …r l v lis 0 : w e t e a ic y w h r spe tt c r n oa x n u e t he m e e 6, hil he l st it it e c o ure t R &D e pe dit r s is o l 0 : T h se …n g su g stf iry st o d x n ue n y 3. e din s g e a l r ng iminish g r t ns, bu in e ur t a he l v lo h …r tt e e ft e m;e t r a x e n lspilo e s a h a g e a e l v lmig tc u t se e ima e l v r tt e g r g t e e h a se he st t s t e a g r t t e e t n fd o x g e a e h x e to imin in r t r s in a g e a e R &D . H o e e , Ko t (19 9 2) ish g e u n g rg t wv r rum e ima e R &D pr d c io f nc io s a h in st y l v la d …n e e g e t rd st t s o u t n u t n tt e du r e e n ds v n r a e iminish g in r t r s, w h t e e ima e o t e e a ic y in t r n e be w e 0 : a 0 : eun it h st t s f h l st it he a g t e n 1 nd 25. D o in ubl g t e t t lr so r e de o e t R &D in a ind st y l a s t a smal rin r a in su c ssf l h oa e u c s v td o n u r ed o le c e se ce u pa e t gt a ad u in fr so r e de o e t &D in apa t ul r…r w u d su g st g t n in h n o bl go e u c s v t d oR r ic a m o l , g e in ta h tdimin ingr t ns c ryo e omo ea g e a e l v l a w l. ish e ur a r v rt r g r g t e es s el ¡1 ¢ F rt r n eo st t s f r», w a st t h r w hr t o his a g fe ima e o ec ne ima et eg o t a eÁ 2 ( 0 + n ) l a v rg n 1 n¸ ta e a e e o me tg e t a ( 0 ) n¸ = 0 : a d Á ( 1 ) n¸ = 3: A lh u h t is q e io mig t mpl y n iv n h tÁ n l 2 n n l 8. t o g h u st n h 25 a a or q ir mo e in o ma io in o de oide t y n , n1, © a l ppe rt e u e r f r t n r rt n if 0 , nd n¸, t e CES f nc io h u t n al w us t e e min h g o t r t r tya af nc io o lo s od t r et e r w h a est ic l s u t n f»: ¡ ¢ ³ h 1 1 i´» » 2 n 1 n¸ 1 © 1 ( 0 + n ) l = 2 ( : 0 2) + ( : 38) 0 0 » 0 0 » U sin t mo o se v t e e ima e o = 0 : se t g R &D a s a e a e l v limpl s a g he stc n r a iv st t f» 6, t in tit v r g e e ie g o t a eo 52%, e a tyt esa r w hr t f2: x c l h mea t e c df r e ima e f o R a ya dR a y s her du e o m st t s r m me n me . O t e st t s w ul h re ima e o dimpl v nl r e r w he e t T h e ima e fd ye e a g rg o t ¤ c s. us, st t so iminishin e u n gr t r s f o mic o d t a e c n e t w h t in r a in g o t t a w se usin r du e o m rm r a a r o sist n it he c e se r wh h t e e g e c d-f r e r ssio s n r ss-c u t yc mpa iso s.15 rge n o co o n r o r n A lho ht ec n e yine ima e r m t od in te t ug h o sist nc st t sf o w ist c mpir a ppr a h s mig tber a r ic la o c e h e ssu - in t…r , t e CES spe i…c t n a v h s se e a isc mf r ingf a u e t a ga st h c a io bo e ide v r ld o o t e t r s h tsho d c st ul a du o bto sr l v nc . T h nit e e a e eCES f n t nc nma c h oa il yinc n mpt ng o t a e u c io a t ht ev l t it o su io r w hr t s o l ifR &D r so c s a e in r d y v l t e t impl d r t o &D l v l be w e pe k ny e ur e r c e ibl oa il ; he ie a io fR e es t e n a a d t o g l v l is g e by n r u h e es iv n µ ¶1 n1 : 38 0 :6 0 = = 1 35:29 n0 :02 0 w ic is impl u y l r e f re e a br a d …n io o h h a sibl a g o v n o d e it n finn v t n a t it . L ik w , fo o a io c iv y e ise r m t e …r r e o d io (1.3), w k o h tt e r t fe uit v l s is pr po t na o t e h sto d rc n it n e n wt a h a ioo q y aue o rio lt h ma g a o u t it fin v t n i.e r in lpr d c iv yo no a io , . µ ¶0: 4 v1 Á 0( 0 ) n : 38 0 : 0 6 = 0 = =7 2 :1 v0 Á ( 1) n : 02 0 T h o e l sint e r t ef c io a o m impo dbyt eCES f n t n;t n yw yt epr bl m ie her st ic iv un t n lf r se h u c io heo l a o g n r t hel wl v lo r w ha c t dw ht o e e a et o e e fg o t sso ia e it hel wpr d c iv yr g o u t it e imeist a ev r e oh v e yf w r so r e d v t d t inn v t n. T h is inc nsist n it t e f c h tc nsu e u c s e o e o o a io is o e tw h h a tt a o mpt n g o t io r w h c n be a mo ze o e e a a g e a e R &D e pe d ur s r ma hig . T h s, t e c n a t a l st r v n s g r g t x n it e e in h u h o st n e a ic y f n t n pr v e a po ra o ima io f rc a a t r gt e a g e a e pr d t n l st it u c io o id s o ppr x t n o h r c e izin h g r g t o uc io ofinn v t n o a io . U n o t a e y t e l e a ur o e s l te g f run t l , h it r t e ¤ r it l uida e a t w t a mo e r a n bl in o a io nc s o ha r e so a e n v t n f n t nmig tl o ik . St l t u c io h o kl e il, hemo e o id sso d lpr v e mer st ic io so h a e r t n nt esh peo h u t n ft ef nc io 15 Itsho d be no e t tt CES f t n Á (n) = © n » is no o ul t d ha he unc io tc nsist n it (1.9 ). N ume ic lsimul t n o e tw h ra a io f t mo e he d lsug e e t ta e a ee o g st d ha v r g mpl yme tin inno a io d cine und rst bil t n, a t ug t e t nto n vt n el s e a iza io l ho h he x e f t c ng d pe he ha e e nds o a dit na r me e a ue n d io lpa a t rv l s. 26 Á(n)t a al w us t g u e w e h r a f n t n t a impl s mo e pl u e v l t it c n h t lo o a g hte u c io h t ie r a sibl oa il y a g n r t a in r a in g o t t a is c n e t w h t e e ima e in R a y a d R a y e e a e n c e se r wh h t o sist n it h st t s me n me . R e alt a h sto de o dit n (1.3) r st ic s t er t tw ic Á 0( )c a g s be w e n c l h tt e…r r rc n io e r t h a ea h h n h n e t en 0 a d n1, sin e n c Á 0( 0 ) v1 n 0 = (3.3) Á ( 1 ) v0 n T h r st ic io t r s o tt is e r t n u n u obe u f lin d t r se u e e miningw e h rmo e pl u e l v l o imin hte r a sibl e es fd - ishing r t r s c n g n r t sig e u n a e e a e ni…c n c e se in g o t . T h r a n f rt is ilu r t d a tin r a s r wh e e so o his l st a e ga r phic lyinFig r al u e2. W ek wt a h r w hr t ( ) n¸ a me av l eo : a me no h tt eg o t a eÁ n l ssu s au f0 2 tso e o me tl v ln a d av l e o 8 a meo he mpl y n e e 1 . Su se t mpl y n e e 0 n au f3: tso t re o me tl v ln ppo hesl pe o o h g o t r t w h r spe tt n e a u t d a 1 , i.e Á 0( 1 ) n¸, is e ua o so r a ft e r w h a e it e c o v l a e tn . n l q lt me e l n mbe . Co sist nc u ra n e yimpo s t ef lo in imito t se h ol w gl n hepossibl a u s o : ev l e fa v0 Á ( 1 )¡Á ( 0 ) n n Á ( 1)¡Á ( 0 ) n n l < a< n¸ ln¸ (3.4) v1 n ¡n 1 0 n ¡n 1 0 v1 F o (3.3), w k o t a tn = n , w ha e Á 0( 0 ) n¸ = rm e n w h ta 0 e v n l a T h t o l e o ig a in . e w in s r in t g v0 a 0 a d n w h t e r spe t e sl pe f r a u re v l pe f ra y po tn n 1 it h se e c iv o s o m n ppe n e o o n ssibl f nc io e u t n ¡1 ¢ n)n¸, a ilu r t dint Á( l s l st a e heFig r . M a imizin ue x gÁ 2 [n + n ] l o e l ssibl aue f 0 1 n¸ v ra lpo ev l so a w a e iv nu rbo ndo o , ec nd r ea ppe u nh wmu ha d io a r w hc ul c d it n lg o t o dbeg ne a e e r t dinamo e dl w ic g n r t s r a n bl v l t it in e u y v l e P r po io 3 e a ish s t is bo n a h h e e a e e so a e oa il y q it au s. o sit n st bl e h ud s v1 af n t n o her t u c io ft a io : v0 v1 0 P r po io 3: IfÁ 0( 0 )= o sit n n Á ( 1) t e n , hn v0 ¡1 ¢ 1 v1=v0 Á 2 [n + n1] l · 0 n¸ Á ( 0 ) n¸ + n l Á ( 1) n¸ n l (3.5) v1 =v0 + 1 v1=v0 + 1 T h bo nd in P r po io 3 is t h , sin e t e e e ist a c n a e pie e ise l e r f nc io e u o sit n ig t c hr x s o cv cw in a u t n Á ( o h h t g o t r t a v r g e o me tis e a ty e u lt he bo d T h s, n)f rw ic he r w h a e ta e a e mpl y n x c l q a ot un . u P r po io 3 is a pr c e ima e o h ma imum po o sit n e ise st t ft e x ssibl in r a in g o t t tc n be e c e se r w h ha a v1 o a e t ru hd bt in d h o g iminishin e u n f rag e l v lo oa il yimpl dby . A tt gr t r s o iv n e e fv l t it ie hesame v0 t , t e r st ic io impl d by (3.3) d e no ime h e r t n ie o s timpo a l w rbo nd o ho mu h g o t se o e u s n w c r wh diminish g r t r c u d g n r t , sin e v l e o a n a e h r o t e d in s in (3.4) in e u ns o l e e a e c au s f e r it e f he n po t ¡1 ¢ impl t e g o t r t a v r g e o me tÁ 2 [n + n ] l is a bit a il co t 0 %. y h r w h a e ta e a e mpl y n 0 1 n¸ r r r y l se o2: 27 λφ(n) a .038 .020 upper bound on v1 increase in growth a v0 from stabilization .002 n Figure 2: Computing Upper Bounds on the Effect of Stabilization P r po io o sit n3t e e o et lsu o l h t e h r w he e t st t dinR a ya dR a y h r f r e l s n yw e h rt eg o t ¤ c se ima e me n me c u d a iseun e a sibl f r l t ns o ol r d rpl u e o mu a io fdimin ingr t ns, no h t e h y in f c o ish e ur tw e h rt e a td . v1 In e ima in h r t st t gt e a io , an t a nc ma kis st c a ur lbe h r o kma k td t hic r ‡e t t v l e r e a aw h e c s he a u v0 o ms o e h c ce Co v n io a st t s, su h a Ch ist n nd Fish r(19 9 8), su g st f…r v rt e y l . n e t n le ima e c s r ia oa e ge t e st n r d v t n o h S&P 500 is o t o d ro 0 %. H o e e , sin e n w…r t n h a da d e ia io ft e n he r e f1 wv r c e ms e d t a emo ev l t ee uit a u s, a dn w…r a el e oh v r oa il q yv l e n e ms r ist dine c a g s a x h n e ndin l d dinst c cu e ok in ic s su h a t d e c s heS&P o yw h al g t is l e yt nl it a , his ik l obea u d r st t ft u oa il y n n e e ima eo r ev l t it in pr …to run ie o e h c ce A s a at r a iv me su e r c l h tv is a w ig t d o ppo t it s v rt e y l . n l e n t e a r , e a lt a e he d o ne isc u t d‡o fpr …t a r ss t et or g s. H e c , t er t fpr …t in t et or g s wo o s c o h w e ime n e h a ioo o s h w e ime v1 se v s a a u rbo d o t e r t r e s n ppe un n h a io . D a a o a t r a c r r t pr …t in t e U .S. t n f e -t x o po a e o s h v0 su g st ast n a d d v t n f r¢ l pr …t fa u 0 ¡1 5%.16 A st n a d d v t n o ge s a d r e ia io o n( o s)o bo t1 a d r e ia io f v1 1: 5 1 1 5% w u d impl ha h a io = ol yt tt er t = 1 :35. Ift est n a d d v t n o is a l w d t h a d r e ia io fv lo e o v0 0:85 v1 bea l r ea 20 %, s ag s w le u l1 :5. Su it in h in o(3.5) y l s il q a bst ut gt is t ie d v0 8 > 2: v 1:5 1 > 27 if 1 = > = 1 :35 ¡ ¢ < v0 0:85 1 Á 2 [n0 + n ] l · 1 n¸ > > v 1:20 > 2: : 36 if 1 = = 1 :50 v0 0:80 Sin et is c l ul t n is in e n n fn a d n1, t ea v st t s impl h td c h ac a io d pe de to 0 n h bo ee ima e yt a iminish g in r t r s t t r l o r a na e v l t it in bo h R &D a in e uit v l s c n st l al w e u n ha ey n e so bl oa il y t nd q y aue a il lo st bil t nt c e seg o t r m 2: % t s mu ha 2: a iza io oin r a r w hfo 0 oa c s 36%, w l it int ema g fe r r e lw h h r ino ro o h e ima e pr v e byR a ya d R a y T h impl s a u rbo d o t e c st o ft e st t s o id d me n me . is ie n ppe un n h o s f bu e y l so : £20 = 5:4% o sin ssc ce f0 27 finit lc n mpt nw nt est n a dd v t no isse ia o su io he h a d r e ia io fv t t 5%, a d 72% w nt est nd r d v t n is e u lt %, bo h o h ha esig i…c n l o1 n : he h a a d e ia io q a o20 t fw ic r n a ty l r e h npr v u e ima e f rt ec st o sin ss c ce W h et e a g rt a e io s st t s o h o s fbu e y l s. il h sebo d su g stt t un s g e ha e ima e inR a ya dR a ya esl h l v r a e , t e on tr l u st t s me n me r ig tyo e st t d h yd o u eo tsigni…c n r w h a tg o t e e t a inc nsist n it e ¤ cs s o e tw h mpir al a sibl l v l o imin in e u n ic lypl u e e e s fd ish gr t r s. Iendmyd u nw ht or ma k Fir , at o g isc ssio it w e r s. st lh u hmye ima e r e t dbye ima in st t sa eid n i…e st t g a t o a e mo e , simil rr su t o a w e I e ima e a t r e a e mo e ha lo s f r w -st t dl a e ls bt in h n st t h e -st t d lt tal w o 16 T his c v r t o e s hesamepe io r d19 5 ¡ 19 9 8. T his e ima ea c un s f rd t e 1 st t c o t o e r ndingimpl d pr duc iv yg o t ie o t it r w h usingc nsumpt n g o t D e r nd o io r w h. t e ingha o yamino s nl rimpa to t st t ft c n hee ima eo hest nd r d v t n, sinc a a d e ia io e ¢ l (pr …t is f rmo e v l t e t n ¢ l (C ). n o s) a r oa il ha n 28 t r eg o t a e Á 0 ·Á 1 ·Á 2 a df rt oc a g s inl v l " ¡" a d" ¡" . Ine ima in h e r w hr t s n o w hne e es 2 1 n 1 0 st t g t et r e a emo e , I o a e h h e -st t d l bt in dane a iv g t epo te ima ef rt o e r w hr t 0 . Sinc in st t o hel w stg o t a e¸ e t c n l g a e r ss is in o e h oo ic lr g e c mpa ibl w h t e mo e , I r pe t d t e min t e it h dl e ae h imiza io un e h t n d rt e c n r in t t ¸0 ¸ 0 . T h e ima e t e w r ¸0 = 0 : 0 0 ; ¸1 = 0 : 22 a d ¸2 = 0 : 36, o st a t ha e st t s h n e e 0 0 n 0 " ¡" = : 0 8, a d " ¡" = ¡ 0 0 1 a d " ¡" = : 0 9. T he d e e c be w e t e l w st 2 1 0 n 1 0 : n 2 1 0 i¤ r n e t e n h o e a d h h st g o t r t is t e sa a in t e t o a e mo l so t e u rbo nd o t e n ig e r w h a e h me s h w -st t de , h ppe u n h in r a in g o t impl d in P r po io 3 w u d be u c a g d B u h t r e a e mo e c e se r wh ie o sit n ol nh n e . tt e h e -st t d is st ln t w rh in se e a e c s. Fir , u l e t e t o a e mo e , itdo s n tpr dic il o e o t y v r lr spe t st n ik h w -st t dl e o e t c u t r y l a r w h " ¡" is po iv , sot tmo er pid g o t is a c t dw h h h r o n e c cic lg o t : 2 1 sit e ha r a r wh sso ia e it ig e c n mpt n l v l T h e ima e f r" ¡" is ne a iv , bu o su io e e s. e st t o 1 0 gt e tis e n ial in ist g ish bl sse t ly d in u a e f o 0 . Se o d itpr v s so e id n e o imin in r t r s, sin e j 2 ¡" j> j 1 ¡" j rm cn , o ide me v e c fd ish g e u n c " 1 " 0 w il j 2 ¡¸1 j< j 1 ¡¸0 j L a l , t e se ue c f t t a c ie e t sma l stme n sq a e he ¸ ¸ . sty h q n e s g h ta h v s he le a ur e r rin t e t r e st t mo e c o ds q it w l it c n e t na ro h h e ae d la c r u e e lw h o v n io lme su e o h bu e a r s ft e sin ss c ce in c n r stw h t et o a emo lw h r q e af ira u to oa il yt y l, o ta it h w -st t de hic e uir s a mo n fv l t it oma c th c n mpt ng o t , e c lyint e19 9 0s w na n a o sumpt ng o t a o sist n l o su io r w h spe ial h he n u lc n io r w hw sc n e ty co oit ist r a v r g f2: %. T h hr e a emo e , o heo he a d a c r sa mo l set sh o ic la e a eo 0 et e -st t d l nt t rh n , c o d l st pe f c l w h N B ER bu e c ce da e T he simu a e c nsu re ty it sin ss y l t s. l t d o mpt n pa h a d c a g s in io ts n h n e c n mpt n f rt e t o a ea d t et r e a emo e r l st a e in Fig r o su io o h w -st t n h h e -st t d la eilu r t d u e3. Se o , at o g h v o u do c nd lh u hI a ef c se ninn v t na hee g o a io st n ineo r w h t esa fg o t , h mebasica g me t ru n c u d be aµ ie t t e f c o c u l t n mo e ol ppl ¶ o h a t ra c mu a io d d lin Se t n 2 in c l a ing a in e me t c io a ibr t n v st n I fnt n Á u c io . T he r a n I c se t f c o R &D is bo h be a e so ho o o us n t c use it se ms t be a e o K mo e r l v n ur e o r w h f rde eo d c u t ie su h a t e U .S., a w l s t e f c r ee a tso c fg o t o v l pe o n r s c s h s ela h a t t a st t s o u v t r in in e me tba d o q e r ssio s a a o be no a d l ss h te ima e fc r a u e v st n se n -r g e n ppe rt isy n e r l bl . St l w a e e st t s t r r in osu a t lc v t e in in e me t sinc e ia e il, h t v re ima e he ea epo tt bst n ia ur a ur v st n , e in e me ta a s t e n v st n ppe r or spo dsosl g ish yt h n e inq I d x r n it t o u in u g l oc a g s . ide pe ime tw hin r d c g a j st n o s t h mo lpr se t d in Se t n 2, a d I c u d g n r t g o t e e t o d u me tc st ot e de e n e c io n o l e e a e r wh ¤ cs n pa it R a y a d R a y u g spe i…c t ns f rÁ ()t a rw h me n me sin c a io o ¢ h tma c e t h mpir a st t s in ic le ima e t e in e me t l e a ur . A s in t e c se w h R &D , t se e ima e t r e o t t r l o h v st n it r t e h a it he st t s u n d u o e y n impl u e v l t it in in e me t H o e e , w c n o e a a e a ish a u rbo d a sibl oa il y v st n . w v r e a nc g in st bl n ppe un simil rt h tin P r po io 3. In t e mo ld v l pe in Se t n 2, t e r t fÁ 0()t r s a ot a o sit n h de e e o d c io h a ioo ¢ un o tt e n o t e v l t it ft e in e me tt o su u od pe d n h oa il yo h v st n oc n mpt n r t . Sin e t is se ie h s a io a io c h rs a st nd r d v t n o bo t1 5%, t is mo e g in c n ms t a e so a e spe i…c t n f r a a d e ia io fa u h d la a o …r h tr a n bl c a io s o t eun e l ingme h n h d ry c a ism ofdiminishingr t nsc na c u tf rt eg o t ¤ e t o u n e e ur a c o n o h r w he c sd c me t d 29 1.20 1.00 0.80 0.60 0.40 0.20 0.00 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 Actual 3 State 2 State (a) Log Consumption - Actual vs. Simulated 0.06 0.05 0.04 0.03 0.02 0.01 0.00 50 52 54 56 58 60 62 64 66 68 70 72 74 76 78 80 82 84 86 88 90 92 94 96 98 -0.01 -0.02 Actual 3 State 2 State (b) ∆ Log Consumption - Actual vs. Simulated Figure 3 byR a ya d R a y w ic in t r impl a g e f r o s o sine c ce me n me , h h un yl r ew la ec st fbu ss y l s. 4 Co cu n . n l sio T h pa re pl r s t e c st o is pe x o e h o s fbu e c ce in a mo e fe d g n u g o t A lh u h sin ss y l s d lo n o e o s r w h. t o g pr v u w r a e pl r d t er l fa g e a e‡u t a io s in mo e s o nd g n u g o t , e io s o kh s x o e h oeo g r g t cu t n d l fe o e o s r w h a d h s e e n t dt a r w h e e t c u d h v n a v n o e h tg o t ¤ c s o l a eimpl a io s f rt ec st o sin ss c ce ic t n o h o s fbu e y l s, t e n t n t tbu e c ce in ov su a t lc st ha y tt h o io ha sin ss y l s v l e bst n ia o s s e obe a l ze f r ly T h nay d o mal . is pa rid n i…e d pe e t s imin in e ur t ish gr t ns oinn v t n a a o a io s nimpo t n h n linal w gbu e ra tc a ne lo in sin ss c ce t e e a e su a t lw la e e e t f rpl u e e y l s og n r t bst n ia ef r ¤ c s o a sibl mpir a o d io s. R e c d f r ic lc n it n du e o m e ima e r m c o o n r o st t sfo r ss-c u t yc mpa iso r nssu g stt a o h .S., t isc a ne o dg n r t g e h tf rt eU h h n lw ul e e a e a inc e se in g o t f o 2: % t 2: n ra r wh r m 0 o 5%, w ic is a c t d w h a in r a in w la e f r h h sso ia e it n c e se ef r o w ic a in iv a o l be w l gt c i…c 1 0 % o h h n d idu lw u d ilin osa r e fhis in ia o mpt n Est t s o it lc nsu io . ima e f diminish gr t r sf o mic od t r o in e u n r m r a aa ec nsist n it h ser d c df r e ima e at o g e tw ht e e u e o m st t s, lh u h t e r q ir impl u y v l t e R &D a d e u y v l e t g ne a e o r e v l t it in hy eu e a sibl oa il n q it a u s o e r t bse v d oa il y c n mpt n g o t St l r st ic io o t e in v t n f n t n t a c o d w h v l t it o su io r w h. il, e r t ns n h no a io u c io h ta c r it oa il y d t lo n in r a in g o t fo 2: % t 36%, w l it in t r ng o st t s fo a aa l wa c e se r wh r m 0 o2: e lw h he a e fe ima e r m c o o n r a aa dw hc n in et e iv rc st fbusin ssc ce h ta ef rl r e h n r ss-c u t yd t n hic o t u od l e o so e y l st a r a a g rt a r po t d in pr v u w r . e re e io s o k Sin et e eis ar a ya e t n el e a u eo t e a io sh be w e g o t a d c ce it c hr le d n x e siv it r t r n her l t n ip t e n r w h n y l s, w ul e …t in oe dw har c p o h tt ispa rc n r t st h it r t r . Fir n o dse m t gt n it e a fw a h pe o t ibu e ot isl e a u e sta d f r mo , ite o e st mph size t ee e to oa il yo r w ht r ug imin a s h ¤ c fv l t it ng o t h o hd ishin e u ns t v st gr t r oin e - me t w e e s pr v u w r a e n , h r a e io s o kh s mpha d t e e e to a iza io o a e a e in e me t size h ¤ c fst bil t n n v r g v st n . T h e pl in w ypr v u w r a ma ec n t gpr d t n o h ¤ e t o a iza io is x a s h e io s o kh s d o ‡ic in e ic io s nt ee c s fst bil t n o g o t , r ‡e t a g n r la n r w h e c ing e e a mbig it o t e e t o u y n he ¤ c s fun e t in y o in e me t T h c r a t n v st n . e mo e e n e h r j sta a d lpr se t d e eis u s mbig o s a u h h o e ic limpl a io s o sine c ce u u bo tt et e r t a ic t n fbu ss y l s o v r g r w hsin et ea e a el v lo v st n a it e iseo alw e na e a eg o t c h v r g e e fin e me tc ne h rr rf l h n‡u t a io s cu t n a e r d c d H o e e , itu a r eue. wv r n mbig o sl pr dic s st bil t n w linc e se g o t a …x d u u y e t a iza io il r a r w h ta e l v lo v st n . Sin ee e e fin e me t c mpir a v n e…nd l tee id n et a oa il ya e t a e a e ic le ide c s it l v e c h tv l t it ¤ c s v r g in e me tr t s a r ss c u t ie t is a a s t v st n a e c o o n r s, h ppe r obet emo er l v n ha e o u y gt e h r ee a tc nn lf rst d in h e e t o sin ss c ce o l n -r n g o t . ¤ c s fbu e y l s n o g u r w h Se o , t is pa re a c nd h pe x mine t e w la e e e t o a iza io r t e ha j stt e e e t o s h e f r ¤ c s fst bil t n a h rt n u h ¤ c s f 30 st bil t no h r w hr t rse Ca r in u h sew la ec l u a io s e pl itysh w a iza io nt eg o t a epe . ry go tt e e f r ac l t n x ic l o s ta h tbu ss c ce c n ma t r T h c n l sio st n in c n r stt h l r e bo y o o k sine y l s a te . is o cu n a ds o t a ot e a g d fw r w ic c mput s o l smalw la e g in f o t v l t it o o su h h o e ny l e f r a s r m he oa il y fc n mpt n o e h bu e io v rt e sin ss c ce A s t e d u n in t e In r d t n r v as, t e in ia o r a io by L u a t t y l. h isc ssio h t o uc io e e l h it l bse v t n c s ha c n mpt n v l t it r m a g e a e‡uc u t n h s n gig ew la eimpl a io se ms t o su io oa il yf o g r g t t a io s a e l ibl e f r ic t ns e o h v l u t bse ue tsc ut y e c ptpe ha w e a ehed p osu q n r in , x e r ps h nsu hsh c s a ebo hv r r e t c o k r t e ype sist n a d h h yv l t e T h is be a se‡u t a io s in a g e a ec nsu n ig l oa il . is cu cu t n g r g t o mpt n in t epo -W a r io h st re a a esu¢c n l r ie tysma lt a h yf ilt e ist ra yimpa tf rr a n bl v r nt c u t n l h tt e a or g e n c o e so a ea e sio o‡u t a io s. B u his d e n timpl t a a iza io c nn tpr d e …r r rw la e e e t t r u h tt os o y h tst bil t n a o o uc sto de e f r ¤ c s h o g o he h n l In a se se t pa rco s t e c ce t a uc s o ig ly be a he use t rc a nes. n , his pe l se h ir l h tL a r inal g n: d h c l ul t n t r u h tbe a sec n mpt n v l t it a n gig ew la ee e t o l is ac a io oa g et a c u o su io oa il yh s e l ibl e f r ¤ c s, n y g o t ma t r B u r wh t e s. tifbu e c ce a e tt pr c ss o o g u g o t in a w y t tis sin ss y l s ¤ c he o e fl n -r n r w h a ha c n e tw h h t ug te pe ime t w ic t is pa ra g s, t yw lma t ra w l. o sist n it is ho h x r n , h h h pe r ue he il t e s el 31 A ppe d n ix P r o fL e o fo mma1: R e alt tt e v l eo c l ha h a u fapa e tis g e by tn iv n · 1 0 Z ¸ · 1 Z ¸ U ( t+ s)d t+ s C C ¡ t s) ½( + ¡ t s) ½( + vt = E t ¼ t+ se d ´E t s ±t+ s¼ t+ se ds t U 0C t) d t+ s ( ¦ 0 I be in by c a a t r g t e e out n o t e d o n f c o t+ s a d o e pe t d pr …t E t [¼ t+ s] g h r c e izin h v l io f h isc u t a t r± n f x ce o s assumin o e n n gg v r me tspe d g r ma s c n a tbe w e t a d t+ s, i.e w e e f ral¿ 2 [t n in e in o st n t en n . hr o l , ;t+ s] G ¿ = G i: 1. F o (1.1), w v rm eha e Y t+ s ¡T c t+ s = j; pj; + s t w ic impl s h h ie Z1 Z1 µ ¶ Y t+ s ¡T l j; + sd = nc t j l n dj 0 0 pj; + s t Z1 = l Y t+ s ¡T )¡ n( l jt d np j 0 Z1 = l Y t+ s ¡T )¡ n( l ms( ¡1 d n¸ j) j 0 Z1 = l Y t+ s ¡T )¡ n( [ms (j)¡1 ] j ¢ d l n¸ 0 = l Y t+ s ¡T )¡(n¸) mt + Áis¡1 ) n( l ( w ee hr Z1 mt+ s = [ms ( j) ¡1 j)¡1 ] E [ms ( ] = 0 T h l stst p u s t e f c h t( t+ s ¡mt)» P o n Á is) T h impl s a l n s t e sa e a e se h a tt a m isso ( . is ie s o ga h me rg e imei pr v il be w e d t s t a d t+ s, e a s t e n ae n · 1 Z ¸ C t+ s = e p x l j; + sd = el ( t¡1 + Á is)( t+ s ¡T ) nc t j (n¸) m Y 0 sot a ht d t+ s C = e l ( t¡1 + Á is) (n¸) m d t+ s Y µ ¶¡° U 0( t+ s) C C t+ s C t+ s 2. U sing t e f c ha h a tt t = , I c mpu e t e r t o o su o t h a io fc n mpt n io . T he U 0 C t) ( Ct Ct g o t o o su r w h fc n mpt n a io tag e in a tis g e by iv n st n iv n Z1 dl t = nC d(nc ) j l jt d 0 Z1 = [( ¡Áid )¢ + Á i ( l j) t d 1 t 0 ¢ nc d ] j 0 Z1 = [( ¡Áid )¢ + Á i (n¸) t d 1 t 0 l d] j 0 = Á i (n¸) t l d sot a s l n s r g h ta o ga e imei pr v il be w e t e a s t e n imet a d t+ s, w h v n e ae C t+ s = C te l Á is (n¸) 3. P r …t ¼ t+ s a e e he q a o ¼ i ifa be t rt c noo y w s no v n e a d 0 ifitw s. Fo o s r it re u lt te e h l g a tin e t d n a r ac n a tl v lo o e n n o st n e e fg v r me tspe d g t e pr ba it t a on wd o e y is ma e be w e n in , h o bil y h tn e isc v r d t en ¡ d t s t a d t+ s is g e by e Á is. H e c , ae n iv n ne ¡ E t[¼ t+ s] ¼ ie Á is = Combin gt e t r e r su t t e pr …t‡o tt in h se h e e l s, h o wa ime t+ s e au t d a c r in o t e r spe t e a d v l a e c o d gt h e c iv n c n it n lo t e sa r g o d io a n h me e imepr v il gbe w e t e a in t e n imet a d t+ s is g e by n iv n 8 > > ¼ i e p(n¸ ( t ¡1 + Ái ( ¡° ) ) ifn e on win o a io a r e n v t n r iv s < x l m 1 s) U 0( t+ s)d t C C o l it ¡ (apr ba it y e Á is e e t vn) ¼ t+ s = U 0 C t) d t ( Y > > : 0 e se l A su ie tc nd io f rvi t ¢c n o it n o obe…n eis f r it o ½ + Ái + ( ¡1 ) n¸Á i > 0 ° l w ic is sa is…e f r° ¸1 . h h t d o D e e zt = en¸( t¡1 + Á i( ¡° ) . Ift e r g …n l m 1 s) h e ime c a g s a ime t+ s, t e w u a e t e v l e o h n e tt h n e pd t h au fm a c r in o c o d gt mt+ s = mt + Á i ( ¡° ) 1 s Itf lo s t a h e ou io o t e h s t ol w gl wo ol w h tt e v l t n fz x ibit hef lo in a fmo io w h ag e r g : t n it in iv n e ime z _t = ¡ it( ¡1 )n¸ Á ° l zt T h au o w in ev l e fo n gapa e tc n t e e o ebec a a t r d by t ef lo in sse q a io tn a h rf r h r c e ize h ol w ga te u t n ½vi (z) = z¼ i + ¹ ( i ¡vj)+ v0( z¡Áivi v z)_ v ° (n¸) 0 z)¡Á ivi = z¼ i + ¹ ( i ¡vj)¡zÁ i ( ¡1 ) l vi ( sow a e asy e o q a io eh v st m fe u t n ( + Á0 + ¹) 0 ( ½ v z)¡¹v1 (z)+ zÁ0 ( ¡1 ) l v00 z) = z¼ 0 ° (n¸) ( ( + Á1 + ¹) 1 ( ½ v z)¡¹v0 (z)+ zÁ1 ( ¡1 ) l v10 z) = z¼ 1 ° (n¸) ( T osov t ea v st m, w u ss l e h bo esy e eg e v0 = ¯0 z v1 = ¯1 z M a c in o ¢c n s y l s t e c e ie t !0 a d !1 r po t d in t et x . ¥ t h gc e ie t ie d h o ¢c n s n e re h et P r o fP r po io 1: I be in by sh w gt a 1 > n . F rsu se n t i.e n ·n . T h n t o fo o sit n g o in h tn 0 o ppo o , . 1 0 e he f c h tN 0 > N 1 impl s a tt a ie L ¡N 1 ¡n > L ¡N 0 ¡n 1 0 sot a 1 > ¼ 0 . Sin en > n a d Á 0( )> 0 , itf lo s t a ( 0 )> Á ( 1 ) In t is c se h t¼ c 1 0 n n ol w h tÁ n n . h a , v0 [½ + ¹ + ( + ( ¡1 ) n¸) ( 1 ) ¼ 0 + ¹¼ 1 1 ° l Á n ] = v1 [½ + ¹ + ( + ( ¡1 ) n¸) ( 0 ) ¼ 1 + ¹¼ 0 1 ° l Á n ] [½ + ¹ + ( + ( ¡1 ) n¸) ( 0 ) ¼ 0 + ¹¼ 1 1 ° l Á n ] < [½ + ¹ + ( + ( ¡1 ) n¸) ( 0 ) ¼ 1 + ¹¼ 0 1 ° l Á n ] ¹ ( 0 + ¼ 1 )+ [½ + ( + ( ¡1 )n¸) ( 0 ) ¼ 0 ¼ 1 ° l Á n ] = ¹ ( 0 + ¼ 1 )+ [½ + ( + ( ¡1 )n¸) ( 0 ) ¼ 1 ¼ 1 ° l Á n ] < 1 H o e e , f o t e …r r e o d io (1.3), n > n ) v0 > v1 , w h is a c n r d t n H e c , wv r r m h sto d rc n it n 0 1 hic o t a ic io . ne n > n . T h e a ish s pa t(1) o h P r po io . F o t e …r r e o d io (1.3), t is aso 1 0 is st bl e r ft e o sit n r m h sto d rc n it n h l impl s v1 > v0 , w ic e a ish s pa t(2). ie h h st bl e r T oe a ish (3), su se t a 1 ¡n > N 0 ¡N st bl ppo h tn 0 1 > 0 , so L ¡N 0 ¡n > L ¡N 1 ¡n 0 1 a d ¼0 > ¼1 . B u h n n tt e , v0 ( + ¹+ ( + ½ 1 ( ¡1 ) n¸) ( 1 ) ¼ 0 + ¹¼ 1 ° l Á n ) = v1 ( + ¹+ ( + ½ 1 ( ¡1 ) n¸) ( 0 ) ¼ 1 + ¹¼ 0 ° l Á n ) ( + ¹+ ( + ½ 1 ( ¡1 ) n¸) ( 0 ) ¼ 0 + ¹¼ 1 ° l Á n ) > ( + ¹+ ( + ½ 1 ( ¡1 ) n¸) ( 0 ) ¼ 1 + ¹¼ 0 ° l Á n ) ¹ ( 0 + ¼ 1 )+ ¼ ( + ( + ( ¡1 )n¸) ( 0 ) ¼ 0 ½ 1 ° l Á n ) = ¹ ( 0 + ¼ 1 )+ ¼ ( + ( + ( ¡1 )n¸) ( 0 ) ¼ 1 ½ 1 ° l Á n ) > 1 w ic c n r d t t a tt a 1 > v0 . H e c , ¼ 1 > ¼ 0 , e a ish g(3). h h o t a ic s hef c h tv ne st bl in T oshow(4), n t t a min lin o o e h tno a c meis g e by iv n Y = ¦+ W = ¼ + L ¡n sot a 1 ¡Y 0 is g e by h tY iv n ¼ 1 ¡¼ 0 ¡( 1 ¡n ) = ( ¡1 ) N 0 + n ¡N 1 ¡n )¡( 1 ¡n ) n 0 ¸ ( 0 1 n 0 = ¡ ( 1 ¡n )¡( ¡1 ) N 1 ¡N 0 ) ¸ n 0 ¸ ( wo h sesig is a n mbig o s sin ew a o l e a ish t a uu c ec n n y st bl ht N 0 ¡N 1 > n ¡n > 0 1 0 w e e s Y 1 > Y 0 o l if h ra ny ¸ N 0 ¡N 1 > ( 1 ¡n )> n ¡n n 0 1 0 ¸ ¡1 It is possibl t g ne a e r su t w e h r t e …r in q ait is a d is n t sa is…e . T h f c t a e o e r t e ls h t e h st e u l y n o t d e at h t C = Y ¡T e a ish s (4). ¥ st bl e P r o fL e o fo mma2: A ppl in y gmypr v u r su t w a e t a o a h r g e io s e ls, eh v h tf re c e imei 2 f ;1 g, 0 ( C) = P i Y i ¡T = ¦i + L ¡n ¡T i = ( ¡1 ) L ¡N i ¡n )+ L ¡n ¡T ¸ ( i i = ¸ ( ¡n )¡( ¡1 ) i ¡T L i ¸ N = ¸ ( ¡n )+ ( ¡1 ) i ¡¸T L i ¸ G T h s, c mpa in o a o su u o r gn min lc n mpt n u de a iza io is g e b io n rst bil t n iv n y ¡ ¢ ¸L ¡¸T ¡¸n G + ( ¡1 ) ¸ G w il v r g o a o mpt n in aw rd o o h st h ea e a en min lc nsu io o l fst c a icsh c s is g e by ok iv n ¸ ¸ ¡1 ¸L ¡¸T ¡ ( ¤( 0 )+ n ( 1 ) n G ¤ G )+ ( 0 + G1 ) G 2 2 1 R e ra g gt e w q a io s a d u gt ef c h tG ¡ 2 ( 0 + G 1 ) itf lo s t a a r n in h set oe u t n n sin h a tt a G , ol w h t ¡ ¢ P C ¤( 0 )+ P C ¤( 1 ) 9 G G > 8 > n¡ ¢< n ( 0 )+ n ( 1 ) ¤ G ¤ G PC G > > > > > G 2 > > > > 2 > > > > > > ¡ ¢ P C ¤( 0 )+ P C ¤( 1 ) = G G < ¡ ¢ ¤ ¤ n ( 0 )+ n ( 1 ) G G PC G = , n G = 2 > > > > 2 > > > > > > ¡ ¢ P C ¤( 0 )+ P C ¤( 1 ) > G G > > ; > ¡ ¢ > > ¤ ¤ : n G > n ( 0 )+ n ( 1 ) G G PC G < 2 2 st bl in h l im. ¥ e a ish gt eca P r o fL e o fo mma3: Simpl d e e t t n y l s e i¤ r n ia io ie d µ ¶ d n Á ( )¡Á 0( ) n nn = 2 d Á() n n n B y c n a it w k o h t o c v y e n wt a Á ( )> Á ( )+ Á 0( ) n 0 nn c 0 ssu io , ol w h tt e iv t eis po iv . ¥ Sin eÁ ( )= 0 by a mpt n itf lo s t a hed r a iv sit e P r o fP r po io o fo o sit n3: T hema imiza io pr bl m c n bee pr sse a x t n o e a x e d s · µ ¶¸ v1 ¢ n ¢ n ma min Á ( 0 )n¸ + x n l a ;Á ( 1 ) n¸ ¡a n l a v0 2 2 A tt e ma imu t e t o e pr ssio s mu h x m, h w x e n stbe e u l sin e ift e a e n te ua, itw u d aw y be q a, c hy r o q l ol l as possibl oinc e set is e pr ssio it e et r a h x e ne h rbyin r a gao c e sin , d pe in nw he pr ssio c e sin rde r a ga e nd go hic x e n a g r l ingf raa h po to q ait a d su it t gba kin y l s t ed sir d r su t ¥ is l r e . Sov o tt e in fe u l y n bst u in c ie d h e e e l . R ee e c s f rn e [1]A be , A n r w 19 8 3. “O pt lIn e me tu d rU n e t in y A me ic n Ec no l de , ima v st n n e c ra t ” ra o mic R e- v w 7 3(1), M a c , p228 -33. ie , rh [2]A g io , P h l h n ilipea d P e e o it , 19 9 2. “A M o e fG r w h t r u h Cr a iv e r - n t rH w t d lo o t ho g e t eD st uc t n” Ec no t ic , 6 io o me r a 0(2), M a c , p323-51. rh [3]A g io , P h l a d G ile Sa t P a l 19 9 8. “V ir u s o B a T ime In e a t n be h n ilipe n l s in u, te f d s: t r c io - t e n P r d c iv yG r w h a d Ec n micFl c u t n M a r e o o we o u t it ot n oo u t a io s” c o c n micD y mic 2(3), na s, Se e pt mbe , p322-44. r [4]A ize ma Jo u n a c a io 19 9 3.“P oic n e t in y P e sist n e a dG r w h n n, sh aa dN n yM r n, l yU c ra t , r e c , n o t” R e ie fIn e n t n lEc n mic 1(2), Jun , p145-6 v wo t r a io a o o s, e 3. [5]A l a e F r a d n U r nJe ma , 19 9 9 . “U singA sse r e t e su et eCo f v r z, e n n oa d ba r nn tP ic s oM a r h sto B u ss Cy l s” M ime , W h ro . sine ce o atn [6 t e n, A n r w a Ch ist ph rP h l n “R e o sid r g t e Co s o u e Cy l s ]A k so d e nd r o e ea c n e in h st fB sin ss ce w hIn o e eM a k t N B ER M a r e o o s A n ua, e e bySt n e it c mpl t r e s” c o c n mic n l dit d a l yFisc e n h ra d Ju ioR o e l t mbe g Ca id ea d L o o : M IT P r ss, p18 7 -207 . r . mbr g n nd n e [7 ]B e u r , P a la a d y u ndCa me a e 19 9 9 .“T h r nP g s, eCo fB u e sto sin ssCy l sa dt eSt bil t n ce n h a iza io V au o ne o me tInsu a e M ime , U n e sit fB r ish Cou l e fU mpl y n r nc ” o iv r yo it l bmia. [8 ]B e n n e B e , 19 8 3. “Ire e sibil y U n e t in y a d Cy l a In e me t Q u re l ra k, n r v r it , c ra t , n cic l v st n ” a t ry Jo n lo o o s; 8 (1), F br r , p8 5-106 ur a fEc n mic 9 e ua y . [9 ]Ca le o R ic r o 19 9 1.“O nt eSig ft eIn e me t n e t in yR e a io sh A me - ba l r , ad , h no h v st n -U c ra t l t n ip” r ic n Ec n micR e ie , 8 1(1), M a c p27 9 -8 8. a oo v w r h, [10]Campbel Jo n a d Jo n Co h a , 19 9 5. “B y F r e o H a : a Co su l, h n h c r ne o c f bit n mpt n-B a d io se Ex a a io fA g r g t o kM a k tB e a io . N B ER W o k pl n t no g e a eSt c re hv r r ingP a r# 49 9 5, Ja ua y pe n r. [11]Ch t e j e Sa y ita D e n Co ba , 19 9 9 . “A W e f r Co a t re , t aj nd a r e la e mpa iso o r - a P o - r n fP e nd st W W II B u e Cy l s: So Impl a io f rt e R oe o o w rM a r e o o sin ss ce me ic t ns o h l fP st a c o c n micP oi- l c s” M ime , U n e sit fP it bu g ie o iv r yo t r h. [12]Ch ist n , L a r n r ia o rya dJo s Fish r “St c a k ta dIn e me tG o dP r e Impl a na e. o kM r e n v st n o ic s: ic - t ns f rM a r e o o s” M ime , N o t w st r U n e sit , 19 9 8 . io o c o c n mic o rh e e n iv r y [13]Cl r , Ke n t , D e e L e ie a d El be h Sy n 19 9 4. “T h Co s o R e e n ak n eh r k sl , n iza t mo s, e st f c ssio ” Ec no o micJo r a , 104(422), Ja u r , p20-36 un l n ay . [14]deH e , P a l 19 9 9 . “O nEn o e o s G r w hU n rU n e t in y In e na io lEc no k u, d gn u ot de c ra t ” t r t na o mic R e ie ;40(3), A u u , p7 27 -44. v w g st [15]D e o , B r d o da L ng a f r ndL a r n eSu we c mme s, 19 88 .“H o o sM a r e o o r wD e c o c n micP oic ¤ e t l yA c O u pu ? B r o in s P a r o Ec no t t” o k g pe s n o micA c iv y 2, p433-8 0. t it , [16 ix , A v sh a d R o r P in y k 19 9 4. In e me t U n r U nc r a t . P r c t n ]D it ina n be t d c, v st n de e t in y in e o : P r c t n U niv r yP r ss. in e o e sit e [17 ]D oma Jim, 19 9 8. “R iskP r f r nc s a dt eW e f r l s, ee e e n h la eCo fB u e Cy l s” R e ie f sto sin ss ce v wo Ec no o micD y a s, 1(3), Ju y p6 -7 6 n mic l , 46 . [18 ]Ea o Jo a h n, 19 8 1. “Fisc lP oic , In t n, a t e A c umu a io o isk Ca a” t n, n t a a l y ‡a io nd h c l t n fR y pit l R e ie fEc no v wo o micSt die 48 (3), Ju y p435-45. u s, l, [19 ]Epst in L a r a d St n e Z in, 19 9 1. “Su it io , R isk A v r n a d t e T e e , ry n a ly bst ut n e sio , n h mpo a rl B e a io fCo su h v ro n mpt na dA sse e ur A nEmpir a n l sis” Jo r a fP oit a io n tR t ns: ic lA a y u n lo l ic l Ec no , 9 9 (2), A pr , p26 6 o my il 3-8 . [20]F t s, A n o io 19 9 8. “D o B u ss Cy l s Ca aa tn , sine ce stL o g Sha w Sh r -R u P e sist nc n do s? o t n r e e a d Ec n micG r w h M ime , IN SEA D . n oo o t” o [21]G r ic e Z v a d A r lP a e 19 84. “P a e t a d R &D a h il h s, i n ie k s, tn s n tt eFir L e e : aFir o k m vl stL o ” inR &D , P a e t a dP r d c iv y e it dbyZ v G r ic e t n s, n o u t it , d e i il h s.Ch a o U n e sit fCh a o ic g : iv r yo ic g P r ss, p55-7 2. e [22]G r ssma , G e ea o n n ndEl a a e pma , 19 9 1. In v t na h n nH l n no a io ndG r w hint eG l ba o - ot h o lEc n o . Ca id e M A : M IT P r ss. my mbr g , e [23]H a l B r n y , Z v G r ic e a d Je r a sma , 19 86 “P a e t a d R a D : Is T h r l, o w n i il h s, n r yH u n . tn s n nd ee aL a ? In e n t n lEc n micR e ie , 27 (2), Ju e p26 g ” t r a io a o o v w n, 5-83. [24]H a t n, R ic r , 19 7 2.“T h r ma ha d eE¤ e t o r ea c s fP ic ndCostU n e t in yo v st n ” Jo r c r a t nIn e me t u - na fEc n micT he r , 5(2), O c o r p258-6. lo o o oy t be , 6 [25]H e pma , El a n a d M a u lT r t n r , 19 9 8 . “A T ime t l n h na n n e aj e be g oSo n aT ime t e p: wa d oR a G r w h B a d o G e e a u po ot se n n r lP r seT e h l g s” G e e a u po c noo ie n r lP r seT e h l g s a d Ec - c noo ie n o nomicG r w h e it d byEl a a H e pma . Ca id e M A : M IT P r ss. o t, d e hnn l n mbr g , e [26 o n a n H u o a M a ia M u ia u r , 19 9 6 “P oic V a ia it a d Ec no ]H pe h y , g nd r n g r ia . ly r bil y n o mic G r w h R e ie fEc n micSt d s, 6 o t ” v wo o o u ie 3(4), O c o r p6 25. t be , 11-6 [27 ]Imr h r gu A y , 19 89 . “Co fB u e Cy l s w hIn iv o oo l , se sto sin ss ce it d isibil ie a dL iq idit it s n u yCo - n st a t Jo r a fP oit a o o , 9 7 (6 D e e r in s” u n lo l ic lEc n my ), c mbe , p136 3. r 4-8 [28 ]Jo s, L a r , R o lo M a uel a d En io St c h t i, 19 9 9 . “T e h oo y (a d P oic ) ne ry dof n li, n n ac et c n lg n ly Sh c s in M o e s o ok d l fEnd g no G r w h M ime , N o t w st r U n e sit . o e us o t ” o rh e e n iv r y [29 ]Ko t m, Sa e , 19 9 2. “In e t n R &D , a d In st y G r w h P h T h sis, Y a e U n ru mu l v n io s, n du r o t” D e l i- vr y e sit . [30]Kr se l P e n A n ho y Smit , 19 9 9 . “O n t e W e f r E¤ e t o imin t u l, ra d t n h h la e c s fEl a ingB u e sin ss Cy l s” R e ie fEc n micD y a s, 2(1), Ja u r , p245-27 2. ce v wo o o n mic n ay [31]L e a , H a n , 19 7 4. “O pt lG r w hinaSt c a icEn ir n n ” R e ie fEc no l nd ye ima o t o h st v o me t v wo o mic St ie 41(1), Ja u r , p7 5-8 6 ud s, n ay . [32]L e h r D a id a d T .N . Sr iv sa , 19 6. “O pt lSa in s U n e n e t in y R e ie v a i, v n in a n 9 ima v g d rU c r a t ” v w o oo fEc n micSt d s, 36 A pr , p153-6 u ie (1), il 3. [33]L u a R o r, 19 7 8 .“A sse r e c s, be t tP ic sinanEx ha g o o ” Ec n me r a 46 ), N o e c n eEc n my o o t ic , (6 v m- be , p1429 -45. r [34]L u a R o r, 19 8 7 . M o e s o u e Cy l s. O x o d B a c s, be t d l fB sin ss ce fr : silB l c w l. a k el [35]M a suy ma Kimin r 19 9 5. “Co e n a it s a d Cu l t e P r c sse in M o l o t a , o i, mpl me t r ie n mu a iv oe s des f M o o l icCo n poist mpe it n Jo na fEc n micL it r t r , 33(2), Jun , p7 01-29 . t io ” ur lo o o eau e e [36 bste d, M a ic , 19 9 4a “Ev l a in isk Co ]O fl ur e . a u t gR y nsumpt n P a h T h R oe o t r e io t s: e l fIn e t m- po a bst u a it ” Eu o a Ec n micR e ie , 38(7 ), A u u , p147 1-8 6 r lSu it t bil y r pe n o o v w g st . [37 ]O bste d, M a r e 19 9 4b. “R isk a in , G l ba iv r a io , a d G r w h A me ic n fl u ic , -T k g o lD e si…c t n n o t” ra Ec no o micR e ie , 8 4(5), D e e v w c mbe , p1310-1329 . r [38 ]O t o , Chir o e , 19 9 9 . “O n M e su in t e W e f r Co fB usin ss Cy l s” M ime , rk st ph r a r g h la e sto e ce o U niv r yo ir in . e sit fV g ia [39 ]P embe t n Ja s, 19 9 6. “T h Co s o R e e n A Co ro , me a e st f c ssio : mme t Ec n mic Jo r a, n” oo un l 106 ), Ju y p9 7 7 -80. (437 l, [40]P embe t n Ja s, 19 9 6 “G r w hT r n s, Cy l a u t a io s, a ro , me b. ot ed cic lFl c u t n ndW ef r it o - la ew hN n Ex c e U t it r f r n e Ec n mic L e t r 50(3), M a c , p387 -9 2. pe t d il yP e e e c s” o o s t e s, rh [41]R a y G a e a d V ae ie R a y 19 9 1. “T e h oo y Co me , ry n lr me , c n lg mmit n nd t e Co fEc - me ta h sto o nomicFl c u t n N B ER W o k u t a io s” r ingP a r# 37 55, Ju e pe n. [42]R a y G a e a d V a e ie R a y 19 9 5. “Cr ss-Co n r Ev e c o t e L in B e w e me , ry n lr me , o u t y id n e n h k t en V oa il ya d G r w h A me ic n Ec no l t it n o t” ra o micR e ie , 8 5(5), D e e v w c mbe , p1138 -51. r [43]R o r D a id 19 9 6 A d a c d M a r e o o s, M c r wH il. me , v , . vne c o c n mic G a l [44]St k y N a y 19 9 5. “R &D a d Ec n mic G r w h R e ie fEc no oe, nc , n oo o t ” v wo o micSt ie 6 ud s, 2(3), Ju y p46-8 9 . l, 9 [45]T a l r i, T h ma 19 9 9 . “R isk Se sit e B usin ss Cy l s” M ime , Ca n g M e l n U n la in o s, n iv e ce o r e ie lo i- vr y e sit . [46 za a H ir f ]U w , oumi, 19 6. “T imeP r f r n ea 9 e e e c ndtheP e o nr seE¤ e tinaT w -Cl ss M o lo c o a de f Ec no o micG r w h” Jo r a fP oit a o o , 7 7 , p6 -52. ot u n lo l ic lEc n my 28