Scientific Research. Vol.1, No.1, May Modern Economy ISSN:

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1 ISSN: Scenfc Research Vol., No., May Modern Economy ISSN:

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3 Modern Economy,,, -58 Publshed Onlne May n ScRes (hp:// TABLE OF CONTENTS Volume Number May Dynamc Ineracve Cycles durng he 8 Fnancal Crss I. M. Neokosmds, V. Polmens Is he Grea Moderaon Endng? G. Canarella, W. S. Fang, S. M. Mller, S. K. Pollard 7 Prce-Seng Mxed Duopoly Models wh Complemenary Goods K. Ohnsh 43 Is Raonal o Mnmze Tax Paymens? A. Löffler, L. Kruschwz 47 Drec Mechansms, Menus and Laen Conracs G. Paser 5 Copyrgh ScRes.

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5 Modern Economy,,, -6 do:.436/me.. Publshed Onlne May (hp:// Dynamc Ineracve Cycles durng he 8 Fnancal Crss Absrac Ioanns M. Neokosmds, Vassls Polmens Deparmen of Economcs, Arsole Unversy of Thessalonk, Thessalonk, Greece E-mal: neokosm@econ.auh.gr, polymen@econ.auh.gr Receved February 6, ; revsed March, ; acceped March 3, Ths paper focuses on he analyss of he 8 fnancal crss and how affecs he global fnancal markes. We analyze hree major markes (US, UK, and ASIA) ha are represened by he levels of hree broad sock ndces S&P 5, FTSE and Hang Seng respecvely. Our mehodology s based on conegraon analyss and Granger causaly es n order o examne he neracon beween he markes (nformaon flows). Addonally, we sudy he volaly ransmsson based on mulvarae GARCH analyss. We fnd sgnfcan changes n nformaon flows before and durng he fnancal crss. Keywords: Un Roo Tes, Conegraon, Granger Causaly, Mulvarae Volaly Processes, Fnancal Crss. Inroducon Due o s surprsng breadh and nensy, he analyss of he 8 global fnancal crss presens a major challenge for economss and fnancal expers. Polcymakers now consder he defnon of key polcy responses and nsuonal rules n order o buld mechansms ha wll conan cross-marke conagon and preven a reoccurrence of he problem n he fuure. Mos of he recen crses sared from emergng markes, whch are presumably more sensve o lqudy shocks because of her underdeveloped and llqud fnancal markes and her large publc defcs. Besdes he 987 crash n Wall Sree ha was echncal and shor-lved n naure, he 8 crss s he frs o be labelled a US crss on he bass ha seems o have sared by he massve US real esae delnquences. An mporan queson relaed o an nernaonal fnancal crss s he exsence of conagon (.e., he nernaonal propagaon of counry- or regon-specfc shocks o oher pars of he world). Accordng o he more open defnon adoped by Forbes and Rgobon [], conagon s measured as any change n he ransmsson mechansms ha occurs durng a volale perod. For example, conagon may esablsh self by a sgnfcan ncrease n cross-marke correlaons. The mos well known fnancal and currency crses ha have occurred over he las 5 years wh global consequences were, he 99 European moneary un problems, he peso effec of 994, and he 997 Asan flu crss (whch also rggered he 998 Russan cold ). The 999 Brazlan devaluaon, he Inerne bubble burs, and he July defaul of Argenna. Ye o dae, here s sll a lo of dsagreemen as o wha are he channels hrough whch fnancal upheaval s ransmed across counres, and on he se of measurable facors ha may be used for he precse denfcaon of a conagon even. Undersandng hese facors s mporan because early recognon of he possbly of conagon may help reduce a counry s vulnerably o exernallyorgnaed shocks. In he wake of he curren fnancal nernaonal crash, growng negraon of fnancal markes has been of heghened neres because such negraon s assumed o generae large, correlaed prce movemens across mos sock markes. Ye due o he complexy and global naure of he curren fnancal crss, s dffcul o move beyond he headlnes of he fnancal press and provde an n deph analyss of he mechansm ha lnks global fnancal markes durng he crss and generaes he phenomenon of conagon. The analyss may ake place on boh he economcs of he crss, as well as on a purely sascal manner. On he economc fron, n he US for example, he fgh has produced wha s ermed a hghly accommodave moneary polcy. Wha s ruly mean by hs decepvely sof phrase s ha snce he onse of he fnancal crss nearly wo years ago, he Federal Reserve has reduced he cos of funds for bg US banks nearly o zero. Ths has happened by adjusng he neres-rae arge for overngh lendng beween banks (he so called Fed-funds rae). Havng brough he Fed-funds rae o almos zero, he US (and laer he UK) swched o he more aggressve polcy of Quanave Easng, whch s also descrbed as Copyrgh ScRes.

6 I. M. NEOKOSMIDIS ET AL. prnng money ou of hn ar. Ths led o an exploson of he sze of he US Fed balance shee, manly hrough he purchase of long-erm secures, nally amed a resarng he flow of cred and o sofen he economc mpac of he fnancal crss for he US. Such acons were no paralleled elsewhere n Europe or Asa so s neresng o undersand he lnkage dynamcs ha were produced. In he curren paper we employ an nuve and sraghforward sascal analyss for esng f conagon occurs by smply comparng cross-marke lnkages beween markes durng a relavely sable perod before he urbulen perod, wh lnkages durng he crss. We examne he shor-run dynamcs of reurns and volaly for socks raded n he US, Brsh and Hong Kong sock exchanges durng he relavely shor las sx year perod. The man focus of he sudy s Granger causaly among he hree markes, whch s a sascal concep of causaly ha s based on predcon. Accordng o Granger causaly, f a marke Granger-causes (or G-causes ) anoher marke, hen pas reurns of he s marke should conan nformaon ha helps predc reurns of he nd above and beyond he nformaon conaned n pas values of he nd marke alone. We frs fnd a srongly sgnfcan conegraon coeffcen for he ndex levels before and durng he fnancal crss perod for all marke pars (US-UK, US-Asa and UK-Asa), whch mples a long run equlbrum level of neracon. We hen proceed o he man fndng of he paper: a change n he drecon of he nformaon flow durng he fnancal crss as hs s esablshed by Granger causaly. As expeced, due o overlappng operang hours and he srong es beween he markes, here s smulaneous neracon beween he US and UK. Snce he Asan markes precede he US wh no overlap, Asan reurns oday ough o nclude an unrevealed componen also presen n yeserday s US reurns. Ye, before he fnancal crss, we can rejec he hypohess of he US marke causng he Asan markes (a a daly level); hs shows a parcularly weak pre-crss neracon. Surprsngly, when we es he null ha US G-causes Asa wh a sample whch ncludes he fnancal crss, we fnd ha he US marke ncludes nformaon abou Asa. Ths provdes evdence of a newly produced channel of nformaon from he US o Asa and, o our knowledge, he frs sascal verfcaon ha he 8 crss was a crss ruly made n he US. The openng of hs new channel of nformaon flow from he US o Asa s a clear ndcaon ha durng he fnancal crss perod he ably of he US markes o produce, capure and dssemnae crss specfc nformaon was unmached by he fnancal markes n oher regons of he world. We fnally move o undersand he volaly ransmsson mechansm over me and across he hree dfferen Ths s also relaed o he non-synchronous radng heory of Lo and MacKnlay []. markes durng he crss. Our mehodology s o examne he dynamc relaonshp beween he daly sock marke reurns and her volales, for he hree markes above, usng a mulvarae generalzed auoregressve condonal heeroskedasc (GARCH) model. Ths s essenally a famly of sascal models orgnally developed by Engle [3-5] and Bollerslev [6,7]. We fnd ha he markes nerac no only n a reurns level bu o some exend hrough volaly spllovers. The UK and Asan markes were nsgnfcanly correlaed before and durng he crss. For he US and Asan markes, changng nformaon flows due o he crss, manfesed hrough Granger causaly for US Asa, s no corroboraed by a change n he sgnfcance of he correlaon coeffcen. Fnally, he US and UK are he only sgnfcanly correlaed markes.. Daa Analyss and Descrpve Sascs The daase used ncludes he closng levels of he daly sock marke ndces for hree major sock markes (US, UK and Hong Kong). We use he S&P 5 ndex for he US, he FTSE for he UK and he Hang Seng ndex as a proxy for he Asan markes. Furhermore, we examne he economercs of hese seres n wo daa samples. The frs sample, wh daa no conamnaed wh he crss, runs from Aprl o Aprl 6;.e., ends before he onse of he fnancal crss. The second sample, from Aprl o Aprl 9, ncludes a leas he frs 8 o monhs of he crss dependng on when one places s begnnng. We compue he daly sock reurns for each ndex as he frs dfference of logarhmc levels. Tables (a) and (b) repor reurn summary sascs for he wo me nervals. Table (a) ncludes he me space before he fnancal crss (FC from now on) and Table (b) presens he resuls of summary sascs ncludng he perod of FC (nd semeser 7-Aprl 9). As we can see from Table (a), Asa gves he hghes mean reurn whle s characerzed by lower volaly wh posve skewness and no excess kuross n compare wh US and UK. US gves he second hgher mean reurn wh he second lower volaly. Addonally, s skewed o he rgh wh no excess kuross. The mos rsky marke s he UK marke n he me nerval before he FC, whle seems o gve he lower mean reurns wh negave skewness and excess kuross. We ge he resuls as hey are shown n Table (b), ncludng he me perod of FC n our analyss. The FC gves he oppose sde of he con whle ASIA, as s represened by he Hang Seng ndex, s shown o be he mos aggressve marke n comparson wh he US and UK. Asa gves he hghes mean reurns wh he hghes sandard devaon, whle remaned skewed o he rgh. US and UK boh exhb negave average reurns when he FC perod s ncluded n he sample. Fnally, all hree markes exhb excess kuross. Copyrgh ScRes.

7 I. M. NEOKOSMIDIS ET AL. 3 Table. Reurn summary sascs for he represenave me seres. (a) Summary sascs for ndex reurns before FC. ASIA US UK Mean Sandard Devaon Skewness Kuross Mnmum Maxmum (b) Summary sascs for ndex reurns durng FC. ASIA US UK Mean Sandard Devaon Skewness Kuross Mnmum Maxmum Mehodology I s well known ha esng for conegraon s a means for correcly esng hypoheses concernng he relaonshp beween wo ndces ha have un roos. In an effor o frsly deermne f he me seres s covarance saonary we employ he Augmened Dckey-Fuller es [8,9] for a un roo. We wll hen es for conegraon. Frsly, we employ a un roo es n order o check for nonsaonary beween our me seres. We hen es for a sgnfcan conegraon coeffcen beween each marke pars. Moreover, we es for Granger causaly n each par of he seres n order o nvesgae he neracon flows among he markes before and durng he fnancal crss me horzon. Fnally we apply a DVEC (, ) model and a CCC model n order o capure he volaly ransmsson by examnng he changes n he correlaon and covarance coeffcens. 3.. Tesng for Un Roos We have o deermne he order of negraon of sock prce seres before we es for conegraon. For hs propose, we consder an Augmened Dckey-Fuller (ADF) es for each of our me seres. So, he es procedure s descrbed by he followng equaons abou he US, UK and Asan markes: k,, US a p US US u k,, UK a p UK UK u k 3 3 3, 3, HS a p HS HS u wh US represenng he log level of he S&P 5 ndex a me, UK represenng he log FTSE and he log level of he Hang Seng compose ndex beng measured n HS 3. I s assumed ha u, ~ d o, u, n all sysem equaons. Fnally, s mporan o noce ha, for he fed error erms u ˆ o be as close as possble o whe nose, we have o selec he correc number of lags based on an nformaon creron such as he AIC []. The null hypohess for he ADF es s ha seres are negraed H : p agans he alernave hypohess of no negraon, H : p -ess n order o accep or rejec he null hypohess of a un roo are performed agans crcal values from he DF-dsrbuon [] and no from he classcal -dsrbuon. Tables (a) and (b) show he es resuls; he null hypohess of nonsaonary canno be rejeced for all he markes and for boh me horzons. So, all me seres (US, UK, HS ) can be assumed o be I() whch means ha we should ake he frs dfference (.e., connuously compounded ndex reurns) n order o acheve saonary. 3.. Tesng for Conegraon We concluded on negraed of order one I() level seres n he prevous secon. In hs secon, we es for conegraon on each par of processes n order o deermne he exsence of long-run equlbra. A sgnfcan conegraon coeffcen mples a long-run equlbrum relaonshp. Then, even hough our daa generang processes conan un roo, hey are gong o move closely ogeher wh he dfference beween hem wll be saonary []. We employ he Engle and Granger es procedure [] n order o es for conegraon: s sep: We have o es f our seres are I(). nd sep: We run he regressons beween (US /UK, US /HS, UK /HS ) n boh perods (before and afer FC). Our regresson models are: US a a UK u () US a a HS u () 3 Clearly hen, ΔUS, ΔUK and ΔHS are he daly reurns of he US, UK and HS ndces. Copyrgh ScRes.

8 4 I. M. NEOKOSMIDIS ET AL. Table (a). Un roo- h lag-es for S&P 5, FTSE and Hang Seng me seres before FC me perod. Un roo es for S&P 5 me seres before he FC me horzon. D-lag -adf bea Y_ sgma -DY_lag -prob AIC F-prob Noes: S&P 5 represens he US fnancal sock marke and he es me nerval s consdered o be from Aprl o Aprl 6. The above resuls were based on PcGve oupu where he selecon crera are obvously shown. Un roo es for FTSE me seres before he FC me horzon. D-lag -adf bea Y_ sgma -DY_lag -prob AIC F-prob Noes: FTSE represens he UK fnancal sock marke and he es me nerval s consdered o be from Aprl o Aprl 6. The above resuls were based on PcGve oupu where he selecon crera are obvously shown. Un roo es for Hang Seng me seres before he FC me horzon. D-lag -adf bea Y_ sgma -DY_lag -prob AIC F-prob Noes: Hang Seng represens he ASIA fnancal sock marke and he es me nerval s consdered o be from Aprl o Aprl 6. The above resuls were based on PcGve oupu where he selecon crera are obvously shown. Copyrgh ScRes.

9 I. M. NEOKOSMIDIS ET AL. 5 Table (b). Un roo- h lag-es for S&P 5, FTSE and Hang Seng me seres ncludng he FC me perod. Un roo es for FTSE me seres durng FC me horzon. D-lag -adf bea Y_ sgma -DY_lag -prob AIC F-prob Noes: FTSE represens he UK fnancal sock marke and he es me nerval s consdered o be from Aprl o Aprl 9. The above resuls were based on PcGve oupu where he selecon crera are obvously shown. Un roo es for S&P 5 me seres durng FC me horzon. D-lag -adf bea Y_ sgma -DY_lag -prob AIC F-prob Noes: S&P 5 represens he US fnancal sock marke and he es me nerval s consdered o be from Aprl o Aprl 9. The above resuls were based on PcGve oupu where he selecon crera are obvously shown. Un roo es for Hang Seng me seres durng FC me horzon. D-lag -adf bea Y_ sgma -DY_lag -prob AIC F-prob Noes: Hang Seng represens he ASIA fnancal sock marke and he es me nerval s consdered o be from Aprl o Aprl 9. The above resuls were based on PcGve oupu where he selecon crera are obvously shown. Copyrgh ScRes.

10 6 I. M. NEOKOSMIDIS ET AL. UK a a HS u (3) 3rd sep: We oban he fed errors uˆ from he above regressons and we es f hey nclude any sochasc rends or no. Then, f we fnd un roos n he resduals we conclude ha here s no conegraon beween he seres. So, we apply an ADF es n he fed errors, k uˆ auˆ buˆ (4) where he null s: H : a agans he alernave, H : a The resuls are shown n Tables 3 and 4, where we rejec he null (no conegraon) a all lags for all marke pars. The fnancal crss does no affec he exsence of long-run relaonshp among he hree markes Informaon Flow Even f he fnancal crss dd no affec he long-run relaonshp of he markes, may sll have affeced he flow of nformaon (he drecon of neracon) beween hem. As we dscussed already, we fnd conegraon beween (US/UK), (US/HS) and (UK/HS) markes. Ye, we don know he drecon of nformaon flow (drecon of neracon) beween he markes. As s well known Granger causaly from X o Y does no ndcae causaly n he proper common use of he erm (.e., does no mply ha he Y seres s he effec or he resul of X seres). Insead, Granger causaly ruly measures precedence and nformaon flow, so ha n our conex here of he recen fnancal crss Granger causaly from a counry X o counry Y mples ha nformaon durng he crss flows from X o Y. Alernavely, we may hnk of developmens n X precedng developmens n Y. Our am n hs secon s o descrbe he dynamc neracon beween he markes and o see he ndependen movemens before we proceed o volaly modellng. I s a crucal aspec of a proper analyss of he crss o analyze he cycle of nformaon before we move o he nex level of volaly analyss. We separae our markes n hree b-varae VAR processes [3] lke followng: US c,us c,ukv (5) UK c,us c,ukv US c, US c, HS HS c,us c,hs (6) UK c,uk c,hs (7) HS c,uk c,hs Alernavely, n he absence of Granger causaly, our seres are generaed by an AR() process as follows: US a p US u (8) HS a p HS u (9) UK a p UK u () We say ha (R, ) reurn seres does no Granger cause (G-cause) he (R j, ) reurn seres f and only f he bes lnear predcon of R j, gven he nformaon se { R,-, R j,- ) does no depend on R,-. Followng he above modellng, we can es he null hypohess agans he alernave: UK does no G-cause US: H : c, H : c, or alernavely, we may say ha under he null hypohess he resdual varances n (5) and (8) above are he same snce ΔUK - does no have any sgnfcance n explanng ΔUS,.e. H : Ev ( ) Eu ( ) H : Ev ( ) Eu ( ) US does no G-cause UK: H : c, H : Ev ( ) Eu ( 3) or H : c H : Ev ( ) Eu ( ), 3 HS does no G-cause US: H : c, H : E( ) E( u ) or H : c H : E( ) E( u ), US does no G-cause HS: H : c, H : E( ) E( u) or H : c H : E( ) E( u ), HS does no G-cause UK: H : c, H : E( ) E( u3 ) or H: c, H: E( ) E( u3) UK does no G-cause HS: H : c, H : E( ) E( u) or H : c H : E( ) E( u ), Esmaon and Tesng We have already descrbed an assumed regresson srucure for our seres. We perform maxmum lkelhood Copyrgh ScRes.

11 I. M. NEOKOSMIDIS ET AL. 7 Table 3. Regresson resuls for he (US/UK), (US/HS) and ( UK/HS) markes before and durng FC horzon. Regresson resuls beween US and UK markes before FC me duraon. Regresson resuls beween US and ASIA markes no FC me duraon. Coeffcen Sd.Error -value -prob Par.R a a RSS: ( ), (R ):.8775 F(, 7) = 43 [.]** Log-lkelhood (478.3); DW: (.66) Νoes: Τhe regresson equaon s US a auk u. US s represened by S&P 5 ndex daa, and UK s represened by FTSE ndex daa. Boh samples of daa are referred o me nerval from Aprl o Aprl 6. Regresson resuls beween UK and ASIA markes before FC me duraon. Coeffcen Sd.Error -value -prob Par.R a a RSS: ( ), (R ): F(, 993) = 4 [.]** Log-lkelhood: (46.89); DW: (.579) Νoes: Τhe regresson equaon s UK a a HS u. UK s represened by FTSE ndex daa, and HS s represened by Hang Seng ndex daa. Boh samples of daa are referred o me nerval from Aprl o Aprl 6. Regresson resuls beween US and ASIA markes before FC me duraon. Coeffcen Sd.Error -value -prob Par.R a a RSS: ( ), ( R ): F(, 993) = 7865 [.]** Log-lkelhood (79.55); DW: (.84) Νoes: Τhe regresson equaon s US a s represened by S&P 5 ndex daa, and HS s represened by Hang Seng a HS u. US ndex daa. Boh samples of daa are referred o me nerval from Aprl o Aprl 6. esmaon (MLE), wh MLE esmaors acually dencal o OLS esmaors. The log-lkelhood funcon for our models, assumng he dn(o,σ ) for he resduals, s of he followng form j log L T /log T /log T / j y, ay, byj, () j,, 3 where ( y, US, y, HS, y3, UK ) and j Coeffcen Sd.Error -value -prob Par.R a a RSS: ( ), (R ): F(,746) = 48 [.]** Log-lkelhood: (547.35); DW: (.35) Νoes: Τhe regresson equaon s US a a HS u. US s represened by S&P 5 ndex daa, and HS s represened by Hang Seng ndex daa. Boh samples of daa are referr ed o me nerval from Aprl o Aprl 9. Regresson resuls beween US and UK markes no FC me duraon. Coeffcen Sd.Error -value -prob Par.R a a RSS: (6. 673), (R ):.8946 F(, 76) =.496e + 4 [.]** Log-lkelhood (5.8); DW: (.88) Νoes: Τhe regresson equaon s US a auk u US. s rep- resened by S&P 5 ndex daa, and UK s represened by FTSE ndex daa. Boh samples of daa are referred o me nerval from Aprl o Aprl 9. Regresson resuls beween UK and ASIA markes no FC me duraon. Coeffcen Sd.Error -value -prob Par.R a a RSS: ( ), (R ): F(, 746) = 58 [.]** Log-lkelhood: (88.9); DW: (.35) Νoes: Τhe regresson equaon s UK a a HS u. UK s represened by FTSE ndex daa, and HS s represened by Hang Seng ndex daa. Boh samples of da a are referred o me nerval from Aprl o Aprl 9. s he resdual varance n he sysem measurng Granger flow from he j h o he h counry defned above. We need o esmae he followng vecor of parameers: (,,, a b j )', j,,3. We can compue he MLE of he above parameer by drecly ulzng he OLS esmaors, whch sasfy he followng varance equaon ˆ T ˆ ˆ ˆ j / T y, ay, b yj, () Copyrgh ScRes.

12 8 I. M. NEOKOSMIDIS ET AL. Table 4. Un roo- h lag-es for obaned resduals by (US/UK), (US/HS) and (UK/HS) regresson equaons. Un roo es for obaned resduals from US-UK regresson seres before FC. D-lag -adf bea Y_ sgma -DY_lag -prob AIC F-prob.79* * * * * ** ** ** ** ** ** Noes: The es maon perod s consdered o be he nerval (Aprl -Apr l 6). The abov e resuls were based on PcGve oupu where he rejecon crera are obvously shown. Un roo es for obaned resduals from US-ASIA regresson seres before FC. D -lag -adf bea Y_ sgma - DY_lag -prob AIC F-prob 3.86** ** ** ** * * ** ** ** ** ** ** Noes: The es maon perod s consdered o be he nerval (Aprl -Aprl 6). The abov e resuls were based on PcGve oupu where he rejecon crera are obvously shown. Un roo es for obaned resduals from UK-ASIA regresson seres before FC. D -lag -adf bea Y_ sgma -DY_lag -prob AIC F-prob.489* ** ** * * * * * ** ** ** Noes: The esmaon perod s consdered o be he nerval (Aprl -Apr l 6). The abov e resuls were based on PcGve oupu where he rejecon crera are obvously shown. Copyrgh ScRes.

13 I. M. NEOKOSMIDIS ET AL. 9 Un roo es for obaned resduals from US-UK regresson seres ncludng FC. D -lag -adf bea Y_ sgma - DY_lag -prob AIC F-prob 3.5** ** ** ** * * ** ** ** ** ** ** Noes: The es maon perod s consdered o be he nerval (Aprl -Aprl 9). The abov e resuls were based on PcGve oupu where he rejecon crera are obvously shown. Un roo es for obaned resduals from US-ASIA regresson seres ncludng FC. D -lag -adf bea Y_ sgma - DY_lag -prob AIC F-prob 3.37** ** ** ** * * ** ** ** ** ** ** Noes: The esmaon perod s consdered o be he nerval (Aprl -Apr l 9). The abov e resuls were based on PcGve oupu where he rejecon crera are obvously shown. Un r oo es for obaned resduals from UK-ASIA regresson seres ncludng FC. D -lag -adf bea Y_ sgma - DY_lag -prob AIC F-prob.636** ** ** ** * * ** ** ** ** ** ** Noes: The esmaon perod s consdered o be he nerval (Aprl -Apr l 9). The abov e resuls were based on PcGve oupu where he rejecon crera are obvously shown. Copyrgh ScRes.

14 I. M. NEOKOSMIDIS ET AL. Based on he a bove, we arrve a he follow ng log- expresson for our sysem lkelhood log ˆ log Lˆ T log T j T (3) We can suppose he same for he unvarae syse m, where our daa are generaed by an AR() model. In hs case he esmaed varance s gven by,, ˆ ˆ ˆ T y a p y ( ) T,, 3 (4) And he correspondng log-lkelhood s gven by: log L ˆ T log T log ˆ T (5) Based on Engle [4] he Wald and LR sascs are asympocally equvalen and we ma y hus use any of wo n order o es for causaly. The lkelhood rao and Wald sascs are gven respecvely as follows: ˆ LR T log ˆ j (6) (cˆ ) j W var(ˆ c ) j (7) Emprcal Resuls Table 5 presens he resuls from he Granger causaly es for all our seres before he fnancal crss (FC perod) and ncludng he fnancal crss (FC) reurns. The major fndng s ha, as we wll explan, nformaon flows and precedence of nformaon have changed when examnng daa before and ncludng he fnancal crss. Specfcally, usng only fnancal daa from he hree markes ha exclude he fnancal crss perod, we observe ha he only wo hypoheses ha are accepable (.e., we canno safely rejec) are ha he US and UK markes canno ransm nformaon o he Hong Kong marke. Ths fndng s very reasonable: wh 8 hours of dfference n local me 4 beween he UK and HS (and 3 hours of dfference n local me 5 beween he US and HS) whle evens ha occur when he Hong Kong marke s open wll be capured by boh HS reurns as well as UK (US) reurns hs s no necessarly rue for nformaon released durng he UK marke hours. The hypohess ha: HS marke does no precede he UK has a p-value of.89 and s rejeced. I wll acually be mpossble for nformaon released durng he US hours 4 7 hours n he summer monhs due o Daylgh savng me n he UK bu no n Hong Kong. 5 hours n he summer monhs due o Daylgh savng me n NY (US) bu no n Hong Kong. Table 5. Res uls for G-cause es; Evdence of changng nformaon flow s durng he Fnancal Crss. Granger causaly es bewe en US and UK mar ke before FC perod. Ho: US-UK T W-Sasc Prob. US does no Granger Cause UK UK does no Granger Cause US Granger causaly es beween US and ASIA marke before FC perod. Ho: US-ASIA T W-Sasc Prob. HS does no Granger Cause US E-7 US does no Granger Cause HS Granger causaly es beween UK and ASIA marke before FC perod. Ho: UK-ASIA T W-Sasc Prob. HS does no Granger Cause UK UK does no Granger Cause HS Granger causaly es beween US and UK marke ncludng FC perod. Ho: US-UK T W-Sasc Prob. UK does no Granger Cause US US does no Granger Cause UK E-7 Granger causaly es beween US and ASIA marke ncludng FC perod. Ho: US-ASIA T W-Sasc Prob. HS does no Granger Cause US E- US does no Granger Cause HS Granger causaly es beween UK and ASIA marke ncludng FC perod. Ho: UK-ASIA T W-Sasc Prob. HS does no Granger Cause UK E- UK does no Granger Cause HS of operaon o ge ncorporaed n same day reurns for he HS and hs s why he hypohess ha HS marke does no precede he US h as a p-value of only -7 and s hu s srongly r ejeced. Whle was very dffcul for nf ormaon o flow from he US o Asa before he crss (p-value of.555) becomes clear ha nformaon does flow from he US o HS when we nclude he FC perod (p-value of.). Ths evdence of a newly produced channel of nfor- maon from he US o Asa s que an amazng fndng and, o our knowledge, he frs sascal verfcaon Copyrgh ScRes.

15 I. M. NEOKOSMIDIS ET AL. ha he 8 crss was ruly made n he US. The dramac openng of hs new channel of nformaon flow from he US o Asa s regsered n he precpous drop of he p-value (775 mes lower han he p-value ha excludes he crss). Ths drop s a clear ndcaon ha durng he fnancal crss perod he ably of he US markes o produce, capure and dssemnae crss spe- nformaon was unmached by he fnancal mar- cfc kes n oher regons of he world. A he same me, due o he operang hours overlap beween he US and he UK, we rejec he null ha US does no nsananeously G-cause UK n boh examnng perods and we conclude ha here s a smulaneous neracon beween he wo markes. Moreover, he Asan marke affecs UK marke bu he oppose s no rue. We are gong o accep (canno rejec) he null of no G-causaly from UK o Asa. Ths means ha whle seems Asa affecs UK, a he same me s no affeced by UK. Ths resul remans sgnfcan durng he FC horzon. Before FC, he Asan marke dd G-cause he US marke bu he oppose flow dd no exs n he sense ha he US marke dd no G-cause Asan markes. When we nclude he FC perod n he analyss, we fnd an nsananeous neracon beween he wo markes, whch means ha we srongly rejec he null of no Granger cause effec. 4. Volaly Lnk beween he Markes In hs secon, we fnally proceed n analyzng he 8 fnancal crss and how s manfesed by changes n he volaly dynamcs of he hree markes. We have already observed ha he markes are co-negraed, whch means ha prce movemens of one marke ndex are srongly relaed o movemens of he oher marke ndces. Ths nerrelaed naure of fnancal markes s a key facor n conemporary fnancal analyss, and s ofen sascally modelled as a mulvarae GARCH me seres model. Such models conan mulple reurn seres of he co-negraed markes, and her man purpose s o faclae he analyss of he varance and co- We use connuously compounded reurns of he hree varance dynamcs among he mulple reurn seres. man marke ndces under sudy: he US ndex S&P 5, he UK ndex FTSE and he Hang Seng ndex for ASIA. We apply he leadng mulvarae GARCH specfcaon, he Dagonal VECH 6 model [5] n order o capure mulvarae volaly dynamcs. We model he reurns as a summaon of a consan and an nnovaon of he seres: r u (8) where r = (r FTSE,, r HS,, r SP, ), μ = (μ FTSE, μ HS, μ SP ), u = (u FTSE,, u HS,, u SP, ). The condonal covarance marx of he nnovaon vecor u, gven he nformaon se, s defned as H Covu. The (p, q)-lag DVECH for volaly modelng assumes a me varyng H ha follows dynamcs defned by, p j - j j H C A u u B H (9) We employ an DVECH (, ) model n order o analyze our seres. Then we ake he followng form of (9): H C A u u BH () where q h,.. H h, h,., h3, h3, h 33, s he covarance marx and s dagonal elemens consue he varance componens of (FTSE, HS, SP) whle he cross producs are he covarance elemens beween he seres. The elemen (h, ) expresses he me varyng correlaon beween (HS, FTSE), (h 3, ) expresses he me varyng correlaon beween (SP, FTSE) and he elemen (h 3, ) expresses he me varyng correlaon beween (SP, HS). The marx (C) conans he consan erms and marces (A, B) conan he ARCH and GARCH coeffcens respecvely 7. We analyze up o seven years of daly daa n order o capure he dynamc volaly process of he mulple reurn seres before and durng he FC perod. The resuls are as follow: Fgures and show he me plo of reurns for each seres before and ncludng he FC perod whle Fgures 3 and 4 show he esmaed volales for connuously compounded reurns for each ndex marke. Moreover, Fgures 3 and 4 presen he me-varyng covarance of DVEC (, ) model for connuously compounded reurns of he hree ndex markes. Furhermore, we saw only he condonal varance and covarance wh he above modellng procedure, bu we have no ye a clear vew abou he correlaon beween he markes and f hey are affeced by he changng drecon of nformaon flows as we descrbed n he prevous secon. I s necessary o es he condonal covarance for sgnfcance, wh a formal srucure of he correlaon coeffcen. Ths es can be done by usng he Consan Correlaon Coeffcen (CCC) model [7] ha s based on he followng specfcaon srucure for condonal covarance: 6 The Dagonal VECH model essenally wres he covarance marx as a se of unvarae GARCH models. 7 For more deals see [6]. Copyrgh ScRes.

16 I. M. NEOKOSMIDIS ET AL. Table 6. Esmaed coeffcens for mean reurn equaon and DVEC (, ) before and durng FC. Mean reurn coeffcen vecor: (μ) Coeffcen Before FC Sd. Error z-sasc Prob. μ fse μ hs.599 μ SP.46 Varance Equaon: H C A u u BH C 9.97E-7 4.7E C 3.48E E C 3.94E-7.38E C 4.6E-7.87E C 3.4E E C E-7. 65E-7 a a a a a a b b b b b b Durng FC Mean reurn coeffcen vecor: ( μ) Coeffcen Sd. Error z-sasc Prob. μ fse μ hs μ SP Varance Equaon: H C A u u BH C.6E-6 3.E C 7.5E-8 3.E C 3.9E-8 7.9E C.6E-6 4.8E C 3.8E-.9E C E-7. 94E a a a a a a b b b b b b Copyrgh ScRes.

17 I. M. NEOKOSMIDIS ET AL RETURNS_FTSE RETURNS_FTSE RETURNS_HS.5 RETURNS_HS RETURNS_S&P 5. RETURNS_S&P Fgure. Connuously compounded reurns of FTSE, S&P 5 and Hang Seng me seres before FC perod. Fgure. Connuously compounded reurns of FTSE, S&P 5 and Hang Seng me seres durng FC perod. Copyrgh ScRes.

18 4 I. M. NEOKOSMIDIS ET AL.. Var(RETURNS_FTSE ).4 Var(RETURNS_HS).6 Var(RETURNS_S&P 5) Cov(RETURNS_FTSE, RETURNS_HS) Cov(RETURNS_FTSE, RETURNS_S&P 5) Cov(RETURNS_HS, RETURNS_S&P 5) Fgure 3. Condonal varance-covarance represenaon of esmaed reurn seres before FC me perod. Var(RETURNS_FTSE ) Var(RETURNS_HS) Var(RETURNS_S&P 5) Cov(RETURNS_FTSE, RETURNS_HS) Cov(RETURNS_FTSE, RETURNS_S&P 5) Cov(RETURNS_HS, RETURNS_S&P 5) Fgure 4. Condonal varance-covarance represenaon of esmaed reurn seres durng FC me perod. Copyrgh ScRes.

19 I. M. NEOKOSMIDIS ET AL. 5 hj, Rj h, hjj,,, j FTSE, HS, SP () If we combne he above fndng wh he G-cause fndngs, we conclude ha he UK and Asan markes The coeffcen (R j ) s he consan correlaon beween he h and j h markes whle he ndvdual marke remaned so durng he Fnancal Crss. On he oher were nsgnfcanly posve correlaed (R ) before and specfc condonal varance followng a one-dmensonal hand, we canno observe any nsgnfcan dfference n GARCH he correlaon (sgnfcan correlaon coeffcen) beween he US and UK (R 3 ) markes whle he cond- hkk, ck aku bk hkk,, k () onal correlaon beween he US and he Asan marke (R 3 ) remans srongly nsgnfcan before and durng he Table 7. CCC esmaon before and durng he FC. FC perod. Thus seems ha nformaon s ransmed n par hrough marke reurns and parly also hrough Before FC volaly spllovers n he case of US/UK. CCC equaon: h c a u b h,, kk k k k kk h R h h j, j, jj, 5. Conclusons Coeffcen Sd. Error z-sasc Prob. C 9.5E-7 3.8E A B C 3.97E-7.58E A B C 3 5.E-7.84E A B R R R Coeffcen Durng FC CCC equaon: h c a u b h,, kk k k k kk h R h h j, j, jj, Sd. Error z-sasc Prob. C 9.5E-7 3.6E A B C.9E E A B C E-7.9E A B R R R An emprcal objecve of hs paper was o examne he exsence and source of he srong ner-marke co-movemens ha are suggesed by fnancal analyss durng he 8 fnancal crss. We analyzed levels and sock reurns for hree ndces (FTSE, Hang Seng and S&P5) ha represen hree major fnancal markes ha consue a major fracon of he world capalzaon. We beleve ha hese hree sock markes are represenave of he European, Asan and US markes respecvely. Afer fndng ha all hree ndces have un roos and hey are conegraed, we performed a hos of Granger causaly ess n order o see he drecon of nformaon flows beween he markes before and durng he fnan- cal crss. The mos surprsng fndng s ha whle was very dffcul for nfo rmaon o flow from he US o Asa before he crss, n formaon dd flow f rom he US o Asa when he crss per od s ncluded n he sample. Ths provdes he frs evdence of a newly produced channel of nformaon and, o our knowledge, s he frs sascal verfcaon ha he 8 crss was ruly made n he US. Moreover, we dd no fnd any sgnfcan correlaon coeffcen, as was mo delled by a CCC model, beween US/ASIA and UK/AS IA markes excep am ong he US and UK. 6. References [] K. J. For bes and R. Rgobon, Co nagon n Lan Amerca: Defnons, Meas uremen, and Polcy Implcaons, Econom a, Vol., No.,, pp [] A. Lo and A. C. Macknlay, An Econome rc Analyss of Nonsynchronous Tradng, Journal of Economercs, Vol. 45, No. -, 99, pp. 8-. [3] R. Engle, Auoregressve Condonal Heeroskedasc- y wh Esmaes of hevarance of U.K. Inflaon, Eco- nomerc a, Vol. 5, N o. 4, 98, pp [4] R. Engle, Arch Seleced Readngs, Oxford Unversy Copyrgh ScRes.

20 6 I. M. NEOKOSMIDIS ET AL. [5] Press, Oxford, 995. R. Engle, The use of ARCH/GARCH Models n Appled Economercs, Journal of Economc Perspecves, Vol. 5, No. 4,, pp [6] T. Bollerslev, Generalzed Auoregressve Condonal Heeroscedascy, Journal of Economercs, Vol. 3, No. 3, 986, pp [7] T. Bollerslev, R. F. Engle and D. B. Nelson, ARCH Models, In: R. Engle and D. McFadden, Eds., Handbook of Economercs, Norh Holland Press, Amserdam, 994. [8] D. A. Dckey and W. A. Fuller, Dsrbuons of he Esmaors for Auoregressve Tme Seres wh a Un Roo, Journal of Amercan Sascal Assocaon, Vol. 74, No. 366, 979, pp [9] D. A. Dckey and W. A. Fuller, Lkelhood Rao Sasressve Tme Seres wh a Un Roo, cs for Auoreg Economerca, Vol. 49, No. 4, 98, pp [] H. Akake, Informaon Theory and an Exenson of he Maxmum Lkelhood Prncple, In: B. N. Perov and Csak, Eds., nd Inernaonal Symposum on Informaon Theory, Academa Kado, Budapes, 973, pp [] R. Harrs and R. Solls, Appled Tme Seres Modellng and Forecasng, John Wley, New York, 3. [] R. F. Engle and C. W. J. Granger, Conegraon and Error Correcon: Represenaon, Esmaon and Tesng, Economerca, Vol. 55, No., 987, pp [3] C. Goureroux and J. Jasak, Fnancal Economercs, Prnceon Unversy Press, Prnceon and Oxford,. [4] R. Engle, Wald, Lkelhood Rao and Lagrange Mul- Economy, Vol. 96, No., pler Tess n Economercs, In: Z. Grlches and M. D. lnrlgaor, Eds., Handbook of Economercs II, 983, pp [5] T. Bollerslev, R. Engle and J. M. Wooldrdge, A Capal-Asse Prcng Model wh Tme-Varyng Covarances, Journal of polcal 988, pp [6] R. Tsay, Analyss of Fnancal Tme Seres, John Wley & Sons, New Jersey, 5. [7] T. Bollerslev, Modelng he Coherence n Shor-Term Nomnal Exchange Raes: A Mulvarae Generalzed ARCH Approach, Revew of Economcs and Sascs, 99. Copyrgh ScRes.

21 Modern Economy,,, 7-4 do:.436/me.. Publshed Onlne May (hp:// Is he Grea Moderaon Endng? UK and US Evdence Absrac Gorgo Canarella,, Wen-Shwo Fang 3, Sephen M. Mller, Sephen K. Pollard Calforna Sae Unversy, Los Angeles, USA Unversy of Nevada, Las Vegas, USA 3 Feng Cha Unversy Tachung, Tawan, Chna E-mal: gcanare@calsaela.edu, gorgo.canarella@unlv.edu, wsfang@fcu.edu.w, sephen.mller@unlv.edu, spollar@calsaela.edu Receved March 3, ; revsed March 5, ; acceped Aprl 5, The Grea Moderaon, he sgnfcan declne n he varably of economc acvy, provdes a mos remarkable feaure of he macroeconomc landscape n he las weny years. A number of papers documen he begnnng of he Grea Moderaon n he US and he UK. In hs paper, we use he Markov regme-swchng models o documen he end of he Grea Moderaon. The Grea Moderaon n he US and he UK begn a dfferen pon n me. The explanaons for he Grea Moderaon fall no generally hree dfferen caegores good moneary polcy, mproved nvenory managemen, or good luck. The end of he Grea Moderaon, however, occurs a approxmaely he same me n boh he US and he UK. I seems unlkely ha good moneary polcy would urn no bad polcy or ha beer nvenory managemen would urn no worse managemen. Raher, he lkely explanaon comes from bad luck. Two lkely culprs exs energy-prce and housng-prce shocks. Keywords: Grea Moderaon, Regme Swchng, SWARCH. Inroducon Tme-seres paerns of real oupu growh, lke many oher economc and fnancal me seres, exhb perods of hgh volaly followed by perods of low volaly. Generalzed auoregressve condonal heeroskedascy (GARCH) models, based on he semnal works of [] and [], accommodae hs phenomenon by explcly modelng he endency for more large (small) changes n he underlyng me seres o follow large (small) changes, hus permng esmaon of he observed volaly cluserng. Problems n esmang GARCH models, however, arse f he underlyng volaly process experences srucural breaks, especally shfs n he overall level of volaly. The emprcal leraure shows ha he sum of he esmaed GARCH coeffcens nearly equals, or even exceeds, one, mplyng a non-saonary varance process (.e., negraed GARCH or IGARCH process). Accordng o [3], hs hgh volaly perssence of shocks n sngle regme GARCH models may reflec srucural changes n he varance process. For example, f hgh, bu consan (homoskedasc), varance for some me swches o a low, bu consan, varance, hen combnng such hgh and low homoskedasc volaly perods produces spurous overall volaly perssence. Tha s, a GARCH model does no dfferenae beween homoskedasc volaly sub-perods, bu denfes hgh perssence and heeroskedascy across he full sample. As such, dsregardng regme changes leads o a msspecfed GARCH model. The msspecfed GARCH model sysemacally oversaed he perssence of volaly shocks (see [4,5]). Commonly, researchers deal wh such srucural breaks by nroducng dummy varables for gven subperods reflecng he change n he level of volaly. For example, Reference [6] develops a es based on he modfed eraed cumulaed sums of squares (ICSS) algorhm (see [7]) and analyzes real GDP growh raes for sx OECD counres (Canada, Germany, Ialy, Japan, he Uned Kngdom, and he Uned Saes) from 96 o 6 and fnd a number of srucural breaks n he daa. The modfed ICSS algorhm, however, suffers from an In early work, Reference [8] nroduces a smlar mehodology for consderng he Grea Moderaon n he US. Copyrgh ScRes.

22 8 G. CANARELLA ET AL. mporan lmaon. To w, denfes exogenously a seres of srucural breaks n he volaly of a me seres, bu assumes ha he volaly remans consan beween he wo break pons. Ye, he analyss uses hese break pons n a model ha explcly recognzes he random naure of volaly. In a seres of nfluenal papers References [9] and [] propose a Markov-swchng echnque o analyze nonsaonary me seres and o model srucural breaks endogenously. Ths approach nroduces a parcularly appealng feaure n ha allows he dang of low versus hgh volaly regmes and, herefore, avods any ad hoc paronng of he sample pah. We apply hs mehodology o analyze, once agan, he Grea Moderaon wh a new ws. Tha s, snce he emergence of he Grea Moderaon, does he low volaly perssence reman unchanged unl he presen? Recen large-scale evens such as worldwde nflaonary pressures and he sub-prme lendng crss may provde a warnng ha he good mes may soon end. The Markovswchng approach can usefully ndcae when oupu growh volaly undergoes shfs from hgh o low and back agan, despe he fac ha he forcng varable causng he regme shfs remans unobservable or unknown. We fnd prelmnary evdence ha sgnals he end of he Grea Moderaon n he UK and he US. The nex secon revews he exsng leraure on he Grea Moderaon. Secon 3 denfes our daa and spells ou our economerc mehodology. Secon 4 repors he resuls of our economerc analyss and nerpres he fndngs. Secon 5 concludes.. Economc Background: he Grea Moderaon The Grea Moderaon emerged as an mporan opc amongs macroeconomss, especally snce he seemngly coordnaed declne n volaly of real GDP growh across numerous developed counres. For example, References [-4] denfy a raher dramac reducon n US real GDP growh rae volaly n he early 98s. Oher auhors, such as [5-7], consder he G7 counres and Ausrala, also fndng a srucural break n he volaly of he oupu growh rae. The breaks, however, occur a dfferen mes n dfferen counres. Smlarly, Reference [8] examnes a sample of OECD counres and demonsraes a consderable declne n he volaly of real oupu growh around he developed world, whle Reference [9] consders a sample of 5 developed and less-developed counres and fnds a leas one break n all bu 9 counres and a mos wo breaks n 6 of he 5 counres, concludng ha shfs n he volaly of he real GDP growh rae occur n many nsances. Furhermore, for he denfed breaks, only one occurs he 97s,, n he 98s, and 9, n he 99s. Several mporan quesons emerge from hese fndngs. Frs, wha caused he declne n volaly? Analyss offer several hypoheses, ncludng beer macroeconomc polces, srucural change, or good luck. For example, [7,] and [] arbue he Grea Moderaon o good luck. Conversely, [] and [3] argue ha a subsanal poron of he Grea Moderaon reflecs beer moneary polcy. The dsncon proves mporan. Good luck can urn no bad luck, whereas, presumably, good polcy does no become bad polcy. Thus, a reurn o bad luck could hrow he economy no he hgh volaly regme, once agan. In [6] he hree commonly proposed explanaons of he Grea Moderaon good moneary polcy, mproved nvenory managemen, and good luck are dscussed a lengh. Good moneary polcy ndrecly affecs he volaly of real GDP growh by provdng a more sable economc envronmen wh lower nflaon and lower nflaon volaly. Improved nvenory managemen provdes an mproved buffer beween producon and sales, whereby he same volaly of sales can exs wh lower volaly of producon. Good luck assocaes wh lower volaly of random shocks o he macroeconomy, such as crude ol prce shocks. The concluson drawn by [6] s ha for he G-7 and Ausrala he evdence suppors he roles good moneary polcy and mproved nvenory managemen, and no good luck n he Grea Moderaon. Second, how does one model he declne n volaly? ) Researchers frequenly adop a GARCH modelng sraegy o capure he movemen n volaly. Much of hs research assumes a sable GARCH process governng condonal growh volaly. The neglec of srucural breaks n he varance of oupu leads o hgher perssence n he condonal volaly. ) Economc growh nvolves long-run phenomena, where for longer sample perods, srucural changes n volaly wll occur wh a hgher probably. Accordng o [3] and [3], he long-run varance dynamcs may nclude regme shfs, bu whn a regme may follow a GARCH process. Ohers, such as [,5,33], and [6] apply hs approach of Markov swchng heeroskedascy wh wo saes o examne he volaly n he growh rae of real GDP. The GARCH modelng approach provdes an alernave o deal wh hs ssue, bu relaxng he mplc assumpon of a consan varance process. A relaed leraure consders me-varyng or Markov-swchng srucural VAR models of he macroeconomy, largely of he US, concludng ha he Grea Moderaon reflecs good luck (e.g., [4-7]). Oher auhors conclude ha he Grea Moderaon reflecs good polcy, usng scky-prce dynamc sochasc general equlbrum (DSGE) models (e.g., [8,9]). However, accordng o [3], srucural VAR models may no provde nformaon on he ssue, as hese models falsely conclude ha good luck and no good polcy can explan he Grea moderaon. Copyrgh ScRes.

23 G. CANARELLA ET AL. 9 3) Reference [6] argues ha he exan mehods of modelng he me-seres properes of he volaly of he real GDP growh rae conan msspecfcaons assocaed wh srucural shfs. 3 They address such msspecfcaons by nroducng srucural shfs n he volaly process, fndng ha he perssence found n GARCH models falls dramacally and even dsappears n some cases. They conclude her paper by sang, The rue es of he cause of he Grea Moderaon may only awa he passage of me. The curren run up n ol prces may provde he acd es. Our fndngs of he end of he Grea Moderaon requred only 5 and 3 addonal quarers of dae for he US and he UK. More mporanly, he dfferen mehodology of regme swchng models uncovered he resul. 3. Model Specfcaon We conduc he emprcal analyss of he dynamcs of he real GDP growh rae for he UK and he US by esmang a seres of unvarae auoregressve non-lnear Markov-swchng models wh wo regmes. The general Markov-swchng model (e.g., [9,], and [39]) nvolves mulple srucures ha can descrbe he me-seres behavor n dfferen regmes and, hus, capure more complex, dynamc paerns. The model s non-lnear, and assumes ha he parameers of he underlyng process of an observed me seres depend on an unobservable (laen) sae varable, descrbng he regmes. Nonlneares arse f processes experence dscree shfs n regmes. By sanconng swchng beween regmes, where he dynamc behavor of he me seres dffers markedly, we can accommodae more complex dynamc paerns. We consder fve specfcaons of he process of oupu growh. To begn, we specfy hree models ha nvolve AR models of order and a wo-sae Markovswchng process. In he frs specfcaon, we assume 3 Accordng o [34], srucural changes may confound perssence esmaon n GARCH models. Tha s, he negraed GARCH (IGARCH) dscussed n [35] may resul from nsably of he consan erm of he condonal varance, ha s, nonsaonary of he uncondonal varance. Neglecng such changes can generae spurously measured perssence wh he sum of he esmaed auoregressve parameers of he condonal varance heavly based owards one. Addonally, Reference [4] provdes confrmng evdence ha no accounng for dscree shfs n uncondonal varance, he msspecfcaon of he GARCH model can bas upward GARCH esmaes of perssence n varance. Includng dummy varables o accoun for such shfs dmnshes he degree of GARCH perssence. Accordng o [36] he IGARCH model makes sense when non-saonary daa reflec changes n he uncondonal varance and Reference [37] shows ha n he presence of negleced parameer change-pons, even a sngle deermnsc changepon, GARCH nappropraely measures volaly perssence. More recenly, Reference [38] argues ha he changes n he varance could arse from changes n he mean, demonsrang ha he esmaed perssence parameer n he GARCH(, ) model conans upward bas when researchers gnore srucural changes n he mean. ha he process of oupu growh depends on wo underlyng regmes, wh consan mean and consan varance n boh regmes. In hs specfcaon, boh he mean, he auoregressve parameer, and he varance depend on he sae, ha s, condoned on he sae such ha a ay u, f S y () a a y u, f S where S denoes he unobserved regme of he sysem. The seres S, =,,, T provdes nformaon abou he regme he economy currenly occupes a dae. If we knew S before esmang he model, we could apply a dummy varable approach. In he Markovswchng approach, however, we assume ha we do no observe S, and we esmae he evoluon of he regmes endogenously from he daa. Furhermore, we assume ha a Markov process governs he ranson beween he wo saes (.e., he probably of resdng n a parcular sae n perod depends only on he sae n perod -). Wh he ranson probables p and q, we summarze he process wh he followng ranson marx: p q P p q where he ranson probables are defned as follows: wh PS ( S ) p, PS ( S ) p, PS ( S ) q, and PS ( S ) q. Assumng condonal normaly for each regme, he condonal dsrbuon of y s expressed as a mxure of dsrbuons: y Na ( ay, ) wh probably Na ( a y, ) wh probably where P S s he condonal probably of beng n regme and s he nformaon se a me -. Ths nformaon se ncludes wo pars. Frs, I denoes he nformaon se ( y, y,... ) ha economercans know. Second, equals he regme pah ( S, S,... ) ha he economercan does no observe. A Gaussan mxure of dsrbuon can provde a flexble approxmaon o a wde class of dsrbuons and can well-approxmae hghly non-gaussan uncondonal dsrbuons [5]. Imporanly, Reference [4] noes ha hs model can generae perssence n he condonal varance process (aggregaed over he regmes) defned as E y E y : S () Copyrgh ScRes.

24 G. CANARELLA ET AL. ( a ay ) ( ) ( ) ( a a y ) ( ) ( a a y ) ( )( a a y ) Assume, for example, ha y depends on wo regmes, a low-varably and a hgh-varably regme. Then, accordng o (3), f he wo regmes are perssen, hs model can suffcenly capure he perssence n volaly of he wo regmes. Conversely, a sngle-regme GARCH model canno capure he perssence ha dffers beween regmes. Consequenly, he GARCH model wll mply overall srong volaly perssence even for homoskedasc varances whn each regme. In [4], he consan-whn-regme varance s found o suffcenly accoun for mos me-volaly of varably. Our second specfcaon ness n specfcaon () and assumes ha he mean and he auoregressve dynamcs depend on he sae, bu ha he varance proves sae ndependen: Tha s, a y a a a y y (3) u f S (4) u f S Our hrd specfcaon also ness n specfcaon () and assumes ha he mean and he auoregressve dynamcs prove sae ndependen, bu ha he varance depends on he sae. Tha s, a ay u f S y (5) a ay u f S For comparson purposes, we also consder our fourh specfcaon, where he rae of oupu growh ( y ) comes from a sngle Gaussan dsrbuon wh mean a ay and varance. Tha s, y a a y u (6) Ths fourh specfcaon ses he null hypohess of no regme swch agans whch we es he alernave regme swches descrbed n he hree alernave hypoheses descrbed n specfcaon (), (4), and (5). A problem arses n Markov swchng models, however, when we es he null hypohess of sngle regme agans he alernave of wo regmes. Under he null hypohess, we canno denfy he saes. Ths volaes he key assumpon ha jusfes he use of sandard lkelhood rao (LR) ess. In hs paper, we employ he non-sandard LR bound es proposed by [4]. The mehod apples emprcal process heory o derve an upper bound for ype I error of a modfed LR sasc under he null, assumng ha we know he nusance parameers under he alernave. Le equal he log-lkelhood under L he alernave and L equal he log-lkelhood under he null, where q parameers exs only under he alernave. Defne he sandard lkelhood rao es as M ( L L). Then, assumng a sngle-leaked lkelhood rao, an upper bound for he sgnfcance of M equals he followng: where P q M exp M / q q M / (7). s he gamma funcon. In he presence of srucural breaks, however, s well- known ha ADF es possesses low power. Does saonary also become regme dependen? In oher erms, do hgh and low volaly regmes exhb dfferen saonary properes? Local, regme-dependen saonary dffers from global, regme-ndependen saonary. Thus, as an alernave es of our regme swchng specfcaons, we can use he Markov-swchng approach o generalze he ADF regresson o accoun for wo dsnc Markov-swchng regmes. Followng he approach proposed by [43], he MS-ADF es equals he followng specfcaon: q y a( S ) b( S ) y ( S ) y u (8) where u equals a N(, ( S )) dsrbuon and S equals he unobservable laen varable ha follows a frs-order Markov process wh consan ranson probably from regme o j. When bs ( ) < for a ceran regme, y s locally saonary. Alernavely, when bs ( ) =, hen y s locally nonsaonary, or locally I(). Clearly, when as ( ), bs ( ), and ( S ) do no depend on he regme so ha as) ( = a, bs) ( = b, and ( S) = and he error erm u does no dsplay regme-dependen heeroskedascy so ha ( S ) =, (8) becomes he sandard ADF regresson. Fnally, conrary o [44], we consder he possbly ha volaly dynamcs may sll exs afer accounng for varance regmes. In [3] a modfcaon of he usual ARCH model s proposed ha allows for changes n regmes, combnng he dea of auoregressve condonal heeroskedascy and he Markov-swchng model (SWARCH). In he SWARCH model, dfferen ARCH processes govern he varance whn boh regmes. Thus, he model conans wo channels of volaly perssence, namely perssence due o shocks and perssence due o regme swchng n he parameers of he varance process. Ths makes regme-swchng ARCH more flexble regardng he esmaon of he volaly perssence of oupu growh compared o he sandard, sngle-regme Copyrgh ScRes.

25 G. CANARELLA ET AL. ARCH model as well o hose models ha swch regmes wh consan varance whn each regme. More specfcally, n our ffh specfcaon, we posulae a SWARCH (,,) model wh wo saes, an AR() specfcaon for y, and a dsurbance followng an ARCH() as follows: y a a y wh I N(, h ) and h b b b S S S where S equals a consan varance facor ha scales he ARCH process, S denoes he low volaly regme, and S denoes he hgh volaly regme. Snce one of he consan varance facors parameers s undenfed, we arbrarly normalze o. Hence, he move from one sae o he oher represens a change n he scale of he ARCH volaly process. An mporan feaure of (9) s ha we equae he parameers of he oupu growh equaon across regmes, whle he varances depend on he sae and dffer across regmes. Ths assumpon smplfes he esmaon and allows us o focus solely on me-varaon n he condonal varance process. 4. Daa and Emprcal Fndngs Ths paper employs quarerly daa on real GDP for he US and he UK obaned from he Inernaonal Fnancal Sascs of he Inernaonal Moneary Fund. We consruc real GDP by dvdng Gross Domesc Produc (GDP) n bllons of naonal currency by he GDP Deflaor ( = ). Boh seres are seasonally adjused. We compue he rae of growh of real GDP, y, as he logarhmc dfference n percenage erms of seasonally adjused quarerly real GDP. The sample perod equals, (9) 957: o 7:4 for he US and 957: o 7: for he UK. Fgure plos he daa and Table repors he uncondonal momens of he daa ogeher wh he Jarque- Bera es of normaly. Over he sample perod, on average, US real GDP grew a a hgher rae han he UK, bu he UK experenced slghly more volaly. Boh seres, however, dsplay sgnfcan lepokuross and non-normaly. We esmae all models by maxmum lkelhood (ML) usng RATS 7. modules. The parameers esmaes repored for he swchng consan-varance models come from usng he BFGS [4,45-47] algorhm, whle he resuls for he swchng ARCH varance models come from usng he BHHH [48] algorhm, as n he laer case we encounered problems of convergence usng he BFGS algorhm. Repored sandard errors are heeroskedascy conssen. In [3] and [39] he erave ML esmaon mehods are dscussed n deal. 4.. Swchng-Mean, Swchng-Varance Model Table summarzes he resuls of he ML esmaon of our frs specfcaon, he swchng n mean and varance model (), where we draw he raes of growh of real GDP from normal dsrbuons ha dffer n mean and varance. In he US, sae exhbs a varance abou wo mes as large as he varance n sae. In he UK, nsead, sae exhbs a varance abou four mes as large as he varance n sae. In boh cases, he esmaed varances prove sascally sgnfcan a he - percen level. In he US, he mean raes of growh of real GDP n sae only slghly exceed hose n sae. Ths reflecs he narrowng gap [] beween he mean growh raes over he busness cycle. Furher, n he US, boh auoregressve coeffcens n sae and sae are sgnfcan; whle n he UK, only he auoregressve coeffcen n sae s sgnfcan. These resuls sugges ha he dynamcs of he UK busness cycle may dffer from ha of he US. Table. Summary sascs. US UK Mean Varance Skewness (.35) (.73) Kuross (Excess) (.) (.) Jarque-Bera (.) (.) No. of Observaons 3 Noe: p-values appear n parenhess under sascs, where approprae. Copyrgh ScRes.

26 G. CANARELLA ET AL (a) US (957: o 7:4) (b) UK (957: o 7:) Fgure. Real GDP growh raes. Copyrgh ScRes.

27 G. CANARELLA ET AL. 3 Table. Parameer esmaes and relaed sascs for swchng-varance, swchng-mean model. US Parameer Esmae -sasc Esmae -sasc a.579* * a.646* * 6.4 a.36** * a.956* * * * * 5.8 P.994* *.96 Q.9945* * Log-lkelhood AIC SIC HQ Dagnosc Tess Sasc p-value Sasc p-value Q (4) Q (8) Q (4) Q (8) Skewness Kuross (excess) Jarque-Bera m Noe: The AIC, SIC, and HQ equal Akake, Schwarz-Bayesan, and Hannan-Qunn nformaon creron. The Q (k) and Q (k) equal Ljung-Box Q-sascs, esng for sandardzed resduals and squared sandardzed resduals for auocorrelaons up o k lags. * denoes % sgnfcance level. ** denoes 5% sgnfcance level. UK 4 Usng a dfferen mehodology, Reference [6] fnds smlar resuls. Table also repors he resuls of a seres of dagnosc ess. Q (4) and Q (8) equal he Ljung-Box sascs for he jon sgnfcance of auocorrelaons of sandardzed resduals for he frs 4 and 8 lags, respecvely, and Q (4) and Q (8) equal he Ljung-Box sascs for he jon sgnfcance of auocorrelaons of squared sandardzed resduals for he same number of lags. Under he null hypohess of zero auocorrelaon, each sasc s dsrbued as a ch-square varable wh 4 and 8 degrees of freedom, respecvely. The Ljung-Box sascs ndcae ha he regme swchng model can successfully capure he seral correlaon n he condonal mean and varance of he US and UK raes of real GDP growh and show no evdence of non-lnear dependences or omed ARCH effecs. Ths fndng s parcularly neresng because growh raes of real GDP show srong ARCH effecs, as wdely documened [49-5]. Furher, he regme-swchng model reduces he excess kuross of sandardzed resduals relave o he excess kuross presen n he acual daa, alhough some degree of lepokuross remans n he UK resuls. 4 The hgh perssence of he regmes, where he ranson probables p and q le close o, proves an mporan feaure of he esmaon. Tha s, hese hgh probables ndcae ha f he economy begns n eher sae or sae, wll lkely reman n ha sae. Fgures and 3 provde a vsual nerpreaon of he resuls, showng how he probably of beng n eher sae or sae evolves over he sample. We base our nference on he full sample and he esmaed ML parameers. We calculae hese smoohed probables, Pr[ S T ] and n conras Pr[ S T] for each quarer based on he knowledge of he complee sample of daa, n conras o he ex ane probables, Pr[ S ] and Pr[ S ], whch we calculae for each quarer based on nformaon avalable up o dae. The smoohed probables provde a relavely objecve mehod of dang major shfs n condonal volaly. In Hamlon [] a drec mehod s proposed for dang regme swches, whereby an observaon belongs o a gven sae f he correspondng smoohed probably exceeds.5. The smoohed probably n Fgures and 3 srongly ndcae he presence of wo regmes. Boh for he US and he UK, he probables reman exremely close o one or zero, ndcang ha he non-lnear fler ha generaes he smoohed probables does reflec an underlyng swchng process raher han smply fng parameers n an ad hoc manner. Copyrgh ScRes.

28 4 G. CANARELLA ET AL (a) US (b) UK Fgure. Smoohed probably of low volaly n sae (swchng-mean and -varance model). Copyrgh ScRes.

29 G. CANARELLA ET AL (a) US (b) UK Fgure 3. Smoohed probably of hgh volaly n sae (swchng-mean and -varance model). Copyrgh ScRes.

30 6 G. CANARELLA ET AL. More specfcally, hese fgures documen he presence of wo sgnfcan srucural breaks boh n he US and he UK economc growh process. In he US case, he frs srucural break occurs n 984:3 and he second akes place n 7:4. On he oher hand, n he UK, he frs srucural break occurs n 99:4 and he second n 7:. These wo daes prove mporan n deermnng he lengh and duraon of he Grea Moderaon n he wo counres. Pror o 984:3 n he US, he probably of sae les numercally exremely close o zero. Ths means ha from he begnnng of he sample hrough 983:3, he US rae of growh of real GDP experences hgh volaly. Begnnng n 984:3, however, he probably of he low-volaly sae swches from.8 n 983:4 o. n 984:, o.47 n 984:, and o.75 n 984:3. From 984:4 o 6:4 hs probably remans above.95, he perod ha concdes wh he Grea Moderaon. Begnnng wh 7:, however, sgns begn o sugges ha he Grea Moderaon may come o an end (see Fgures and 3). The probably of he low-volaly sae sars o declne, n a fas and swf manner. In 7:, he probably of sae falls from nearly one o.9. Ths probably declnes furher o.86 n 7:, hen o.75 n 7:3 and fnally o.59 n 7:4. Whle echncally sll greaer han.5, hs evdence pons o he begnnng of he end of he Grea Moderaon era n he US. The evdence favorng he endng of he Grea Moderaon appears sronger n he UK case. In 99:4, he probably of sae ncreases o.8 from. n he prevous perod and remans close o.99 unl 6:4, a whch me he frs slgh declne occurs, from.98 n 6:3 o.93 n 6:4. Ths probably declnes dramacally n he nex wo quarers, o.76 n 7: and. n 7:, he end of he sample perod for he UK. 4.. Consan-Mean, Consan-Varance Model Table 3 repors he esmaes of he lnear AR() sngleregme consan-varance model, our fourh specfcaon (6), and relaed dagnosc sascs. Clearly, he model does a poor job of modelng he volaly of boh he US and he UK growh raes of real GDP. The dsrbuon of he sandardzed resduals exhbs heavy lepokurcy and dsplays a sgnfcan deparure from normaly. Furhermore, sgnfcan evdence emerges of second-momen nonlnear dependences n he sandardzed resduals. As noed by [39], he sngle-regme model effecvely averages he varance over he sample perod so ha he model does a poor job of descrbng he daa n eher regme. Ths, n urn, nduces posve seral correlaon n he sandardzed squared resduals, as oversaes he varance n he low-varance regme and undersaes he varance n he hgh-varance regme. Table 3. Parameer esmaes and relaed sascs for sngle-regme, consan-varance model. US Parameer Esmae -sasc Esmae -sasc a.5736* * a.885* * * Log-lkelhood AIC SIC HQ Dagnosc Tess Sasc p-value Sasc p-value Q(4) Q(8) Q(4) Q(8) Skewness Kuross (excess) Jarque-Bera Noe: The AIC, SIC, and HQ equal Akake, Schwarz-Bayesan, and Hannan-Qunn nformaon creron. The Q (k) and Q (k) equal Ljung-Box Q-sascs, esng for sandardzed resduals and squared sandardzed resduals for auocorrelaons up o k lags. * denoes % sgnfcance level. ** denoes 5% sgnfcance level. UK Copyrgh ScRes.

31 G. CANARELLA ET AL. 7 As prevously noed, he es of he null hypohess of a sngle-regme consan-varance model agans he alernave of a regme-swchng model s no sraghforward. Under he null, only one regme exss n fac ha governs he rae of growh of real GDP. Thus, we canno denfy he regme sayng probables p and q. Ths makes he asympoc dsrbuon of he usual ess (lkelhood rao, Wald and Lagrange mulpler) no longer ch-square [4,5,53]. To nerpre he lkelhood rao sascs, we appeal o he mehods n [5]. Tesng he null of sngle regme agans he alernave of a swchng regme mples ha r = 3, where r equals he number of resrcons (.e., =, = a, and a a a = ). From (7), we can calculae ha he.5 (.) upper bound requres a value of.94 (6.9), raher han he convenonal ch-square value of 7.8 (.3). Values exceedng hs upper bound sugges rejecng he null hypohess. The LR es sascs for he US equals 49.5 and for he UK,.8. These numbers mply ha we rejec he null n boh cases, even afer nvokng he upper bound n [4]. Thus, hese resuls provde srong evdence n favor of he wo-sae regme-swchng specfcaon for he growh raes of real GDP of he US and he UK Swchng-Mean, Consan-Varance Model Table 4 repors he ML esmaes of he swchng-mean, consan-varance model, our second specfcaon (4), (.e., a a, a a, bu = ). The large dfference n mean growh raes beween he wo regmes provdes he mos conspcuous feaure of he esmaes. The esmaes of he ranson probables mply ha he probably of remanng n he low volaly sae remans exremely hgh for boh he US and he UK. The suaon dffers for sae. The probably n he US ha sae wll perss for more han one quarer equals only.757, whle he probably n he UK ha sae wll perss for more han one quarer equals a value abou four mes as hgh. Fgures 4 and 5 show how he smoohed probably of resdng n eher sae or sae evolves over he sample. The evdence n Fgure 4 ndcaes ha when he probably of resdng n he low volaly sae devaes from, does so for a shor perod of me. The fgure reflecs hs n he sharp spkes a rregular nervals, especally durng he md and lae sevenes, he early eghes, and he early nnees. The swchng-mean model mproves over he sngle-regme, con- Table 4. Parameer esmaes and relaed sascs for swchng-mean, consan-varance model. US Parameer Esmae -sasc Esmae -sasc a.749* *.83 a.3946* * 3.7 a.33* **.785 a.554** * * * p.959* * q.757* **.3 Log-lkelhood AIC SIC HQ Dagnosc Tess Sasc p-value Sasc p-value Q(4) Q(8) Q (4) Q (8) Skewness Kuross (Excess) Jarque-Bera Noe: The AIC, SIC, and HQ equal Akake, Schwarz-Bayesan, and Hannan-Qunn nformaon creron. The Q (k) and Q (k) equal Ljung-Box Q-sascs, esng for sandardzed resduals and squared sandardzed resduals for auocorrelaons up o k lags. * denoes % sgnfcance level. ** denoes 5% sgnfcance level. UK Copyrgh ScRes.

32 8 G. CANARELLA ET AL (a) US (b) UK Fgure 4. Smoohed probably of sae (swchng-mean, consan-varance model). Copyrgh ScRes.

33 G. CANARELLA ET AL (a) US (b) UK Fgure 5. Smoohed probably of sae (swchng-mean, consan-varance model). Copyrgh ScRes.

34 3 G. CANARELLA ET AL. san-varance model. The log-lkelhood funcon ncreases slghly n he US and he UK from o and from 8.64 o , respecvely. Furhermore, he swchng-mean model capures a dvergen paern dsplayed by he auoregressve dynamcs of oupu growh as he auoregressve coeffcen n hgh-volaly sae s wce as large as n low-volaly sae. Ths resul has mporan economc mplcaons as suggess ha he auoregressve dynamcs of oupu growh vares along he busness cycle. The model remans dsncly nadequae, however, as sll evdence exss of second-momen dependences, lepokurcy, and non-normaly n he sandardzed resduals. We can easly es he null hypohess of he swchng-mean, consan-varance model agans he alernave of he swchng-mean and -varance model. Tha s, he LR es sasc, ch-square dsrbued wh one degree of freedom under he null, equals for he US and 93.5 for he UK, provng sgnfcan a usual levels. We, hus, rejec he resrced swchng-mean, consan varance model n favor of he unresrced swchng-mean and -varance model Swchng-Varance, Consan-Mean Model Table 5 repors he ML esmaes of he swchngvarance, consan-mean model, our hrd specfcaon (5), (.e., a = a, a = a, bu ). The esmaes of and show ha n he US, he varance of oupu growh s abou wo mes as hgh n hgh- volaly sae as n low-volaly sae, whle n he UK, s abou four mes as hgh n sae as n sae. The esmaes of he ranson probables show ha boh saes mply exreme perssence. Ths conrass wh he resuls of he specfcaon wh swchng-mean, consan-varance model, where he ranson probably of sae dd no ndcae perssence. Fgures 6 and 7 llusrae he smoohed probables of saes and. The graphs prove que dssmlar o he graphs n Fgures and 3. An exended perod of hgh volaly exss followed by a perod of low volaly. Based upon Hamlon s dang mehod, he perod of low volaly sars n 984: for he US, as he smoohed probably of low-volaly sae ncreases o.6, a value whch, for he frs me, exceeds.5. Conversely, for he UK he perod of low volaly sars laer, n 99:3, as he smoohed probably of sae ncreases o.74 for he frs me snce he begnnng of he sample. The pecular feaure of he Fgures, however, does no res wh he dang of he begnnng of he Grea Moderaon, whch receved much aenon n he appled economerc leraure. Raher, ress wh he dang of he end of ha perod. A dealed scruny of he pah of he probably of low-volaly sae ndcaes ha n he US, he probably of sae declnes begnnng n 7:. More specfcally, he probably of Table 5. Parameer esmaes and relaed sascs for swchng-varance, consan-mean model. US UK Parameer Esmae -sasc Esmae -sasc a.5578* * a.77* * * * * P.994* * Q.9945* * Log-lkelhood AIC SIC HQ Dagnosc Tess Sasc p-value Sasc p-value Q(4) Q(8) Q (4) Q (8) Skewness Kuross (excess) Jarque-Bera Noe: The AIC, SIC, and HQ equal Akake, Schwarz-Bayesan, and Hannan-Qunn nformaon creron. The Q (k) and Q (k) equal Ljung-Box Q-sascs, esng for sandardzed resduals and squared sandardzed resduals for auocorrelaons up o k lags. * denoes % sgnfcance level. ** denoes 5% sgnfcance level. Copyrgh ScRes.

35 G. CANARELLA ET AL (a) US (b) UK Fgure 6. Smoohed probably of sae (swchng-varance, consan-mean model). Copyrgh ScRes.

36 3 G. CANARELLA ET AL (a) US (b) UK Fgure 7. Smoohed probably of sae (swchng-varance, consan-mean model). Copyrgh ScRes.

37 G. CANARELLA ET AL. 33 low volaly goes from.9 n 7: o.85 n 7:, o.75 n 7:3, and o.58 n 7:4. In he UK, he evdence ha Grea Moderaon ended appears even more srkng. The probably of low varably n 6:4 equals.94, bu n 7: drops o.76, and n 7: o.. Unlke he swchng-mean, consan-varance model, we canno rejec he resrced swchng-varance, consan-mean model n he US case n favor of he unresrced swchng-mean and -varance model. The LR es sasc, ch-square dsrbued wh wo degree of freedom under he null, equals.5556, whch s no sgnfcan. In he UK, however, he LR es sasc equals 4.754, whch s sgnfcan a usual levels. Thus, we can rejec he swchng-mean, consan- varance model for boh he US and he UK n favor of he swchng-mean and -varance model, bu we can only rejec he swchng-varance, consan-mean only for he UK. The resuls of our analyss sugges ha he growh of real GDP for he US and he UK exhb Markovswchng behavor. Based on he evdence of a wo-sae Markov-swchng dynamcs, he ssue, however, arses wh respec o he saonary of he wo growh-rae seres. Accordng o he sngle-regme sandard ADF es sascs, he wo seres prove saonary. The ADF sascs (wh nercep and lags on he dfferences) equal.5358 and 5.57, respecvely, for he US and he UK Regme-Swchng Saonary Tess Table 6 repors he esmaon resuls for he swchng regme ADF es (8) for q = (.e., a swchng regme DF es). Srong evdence emerges o suppor locally saonary oupu growh n boh he US and he UK. The esmaes of b and b boh prove negave n he hgh and low volaly regmes, and he assocaed - values far exceed n absolue value he Dckey-Fuller sascs. Noe, however, ha hese -values do no follow he Dckey-Fuller dsrbuon. In [43] Mone-Carlo mehods are used o calculae he p-values for he -sascs. We do no pursue hs approach for wo reasons. Frs, we srongly rejec he sngle-regme ADF n favor of Markov swchng ADF. The maxmzed values of lkelhood funcon for he sngle regme ADF equals 55.8 and 8.6 for he US and he UK, respecvely. Consequenly, he LR es sasc equals 5.68 for he US, whle for he UK, equals Thus, we can clearly rejec he null n boh cases even afer nvokng Daves upper bound. Second, boh regmes prove locally saonary, vasly dfferen from he resuls obaned by [3]. Furhermore, our man neres les n dang he wo regmes. From hs vewpon, he resuls of he Markov swchng ADF regressons corroborae he dang evdence on he Grea Moderaon prevously obaned. Fgures 8 and 9 plo he smoohed probables. Table 6. Parameer esmaes and relaed sascs for he markov-swchng un-roo model. US UK Parameer Esmae -sasc Esmae -sasc a.575* * a.5975* * 6.9 b.7633* * b.78* * * * * * 7.96 p.994* * q.9945* * Log-lkelhood AIC SIC HQ Dagnosc Tess Sasc p-value Sasc p-value Q(4) Q(8) Q (4) Q (8) Skewness Kuross (excess) Jarque-Bera Noe: The AIC, SIC, and HQ equal Akake, Schwarz-Bayesan, and Hannan-Qunn nformaon creron. The Q (k) and Q (k) equal Ljung-Box Q-sascs, esng for sandardzed resduals and squared sandardzed resduals for auocorrelaons up o k lags. * denoes % sgnfcance level. ** denoes 5% sgnfcance level. Copyrgh ScRes.

38 34 G. CANARELLA ET AL (a) US (b) UK Fgure 8. Smoohed probably of sae (swchng-adf model). Copyrgh ScRes.

39 G. CANARELLA ET AL (a) US (b) UK Fgure 9. Smoohed probably of sae (swchng-adf model). Copyrgh ScRes.

40 36 G. CANARELLA ET AL. They also show ample evdence for regme changes n he real GDP growh rae. Such changng-perssence behavor would no emerge from he sandard un-roo ess, whch assume perssence remans consan hrough he sample sub-perods. The daes of he begnnng and endng of he Grea Moderaon nearly mach hose obaned usng he Markov-swchng models. Based upon Hamlon s dang mehod, he perod of low volaly sars for he US n 984:3, as he smoohed probably of sae ncreases o.76 and ends n 7:3 as he smoohed probably of low varably decreases o.4. Ths declne s mmedaely followed n 7:4 by a furher sharp decrease o.5. For he UK, nsead, he daes of he begnnng and endng of he Grea Moderaon are slghly dfferen from he ones deeced by he Markovswchng model. The Markov swchng ADF regresson places he begnnng of he Grea Moderaon on he las quarer of 99 raher han he hrd quarer of 99. The Markov-swchng ADF regresson does no dae he end of he Grea Moderaon n he UK, bu hns a, as he probably of low varably declnes from.94 n 7: o.74 n 7: Auoregressve Condonal Heeroskedasc Varance Markov Regme-Swchng Model We now relax he assumpon of consan varance whn each regme and allow he condonal varances o follow a swchng ARCH () process-swarch(), our ffh specfcaon (9). We use he AIC creron o choose he SWARCH () srucure. Table 7 repors he esmaes for he sngle-regme verson of he model. The auoregressve parameers nearly mach hose repored for he consan varance regme-swchng model. The condonal-varance parameers prove sascally sgnfcan, as expeced. For he US, however, he sum of he ARCH esmaes b + b falls sgnfcanly below uny, whch sasfes he saonary assumpon. Conversely, for he UK, a Wald es suppors he volaon of he saonary assumpon, whereby he condonal varance follows an negraed ARCH and b + b =. The Wald es sasc, dsrbued ch-square() under he null, equals.66, whch proves nsgnfcan a any usual level (p-value =.797). Table 8 repors esmaes of he regme-swchng AR ()-ARCH () model. Resuls reman vrually unchanged for hgher ARCH (3) or lower ARCH () lags of he ARCH process. The srkng feaure of he resuls suggess ha alhough he saes reman hghly perssen, he underlyng fundamenal ARCH () process does no. Tha s, he volaly effecs as revealed by he swchng ARCH esmaes do no exhb hgh perssence. Ths reflecs he esmaes of he decay parameer, = b + of he ARCH processes. The volaly effecs for b Table 7. Parameer esmaes and relaed sascs for he sngle-regme, AR ()-ARCH () model. US UK Parameer Esmae -sasc Esmae -sasc a.5969* * a.337* b.955* * b.49* * 3.8 b.4765* **.48 Log-lkelhood AIC SIC HQ Dagnosc Tess Sasc p-value Sasc p-value Q (4) Q (8) Q (4) Q (8) Skewness Kuross (excess) Jarque-Bera Noe: The AIC, SIC, and HQ equal Akake, Schwarz-Bayesan, and Hannan-Qunn nformaon creron. The Q (k) and Q (k) equal Ljung-Box Q-sascs, esng for sandardzed resduals and squared sandardzed resduals for auocorrelaons up o k lags. * denoes % sgnfcance level. ** denoes 5% sgnfcance level. Copyrgh ScRes.

41 G. CANARELLA ET AL. 37 Table 8. Parameer esmaes and relaed sascs for he markov regme-swchng AR ()-ARCH () model. US UK Parameer Esmae -sasc Esmae -sasc a.5663* *.57 a.35* b.775* *.9659 b b p.994* * q.9945* * * * Log-lkelhood AIC SIC HQ Dagnosc Tess Sasc p-value Sasc p-value Q (4) Q (8) Q (4) Q (8) Skewness Kuross (excess) Jarque-Bera Noe: The AIC, SIC, and HQ equal Akake, Schwarz-Bayesan, and Hannan-Qunn nformaon creron. The Q (k) and Q (k) equal Ljung-Box Q-sascs, esng for sandardzed resduals and squared sandardzed resduals for auocorrelaons up o k lags. * denoes % sgnfcance level. ** denoes 5% sgnfcance level. he US swchng ARCH model de ou n abou 3 quarers (.39 ), whle hose of he sngle-regme 3 ARCH model perss for more han hree years (.4 ). Conversely, he volaly effecs for he UK swchng ARCH model de ou n abou 4 quarers 4 (.4 ). We noe, however, ha he ARCH erms n he sngleregme model prove hghly sgnfcan whle n he swchng-regme model, hey lose her sgnfcance. In he swchng-arch model of (9), changes n he regme do no affec he dynamcs of he process, jus he scale [3,54,55], whch reflecs he parameer. The esmaes of hs parameer ndcae ha for he UK, he condonal varance n he hgh volaly sae exceeds he low-volaly sae by more han mes. For he US, nsead, hs rao equals abou 5. The resdual dagnoscs clearly ndcae ha no evdence exss of secondmomen nonlnear dependences n he sandardzed resduals. In fac, he auoregressve coeffcens for he ARCH() models n boh regmes prove nsgnfcanly dfferen from zero. Ths suggess a homoskedasc error process, whch maches he fndngs of [6]. They repor ha he GARCH and ARCH processes dsappear once dummy varables capure he shf from hgh o low-volaly regmes. A LR es rejecs he sngle-regme consan-varance model n favor of he sngle-regme ARCH model. The LR es sasc, dsrbued as ch-squared wh wo degrees of freedom under he null, equals n he US and n he UK, whch proves sgnfcan a any usual level. The regme-swchng AR()-ARCH() model yelds sgnfcanly hgher log lkelhood values han he sngle-regme AR()-ARCH(). So, we unambguously rejec he null of no Markov swchng by he Daves upper-bound es. The LR es sascs, dsrbued as ch-squared wh one degree of freedom under he null, equal and for he US and he UK, respecvely. These values, even afer nvokng Daves s upper-bound adjusmen, prove hghly sgnfcan. Thus, whle he applcaon of he sngle-regme ARCH model leads o nearly non-saonary varance processes, he use of he Markov-swchng ARCH model subsanally mproves he resuls. The resuls of he SWARCH model furher confrm he prevous daes of he begnnng and end of he Grea Moderaon. The smoohed probables for he low- and hgh-volaly regmes (saes and, respecvely) follow very closely he resuls found whou he ARCH componen. Fgures and llusrae hs pon. Based on Hamlon s dang mehod, he swchng- ARCH model capures reasonably well he perod of he Grea Moderaon. The low-volaly regme sars n he US n 984:, as he smoohed probably ncreases o Copyrgh ScRes.

42 38 G. CANARELLA ET AL (a) US (b) UK Fgure. Smoohed probably of sae (swchng-arch model). Copyrgh ScRes.

43 G. CANARELLA ET AL (a) US (b) UK Fgure. Smoohed probably of sae (swchng-arch model). Copyrgh ScRes.

44 4 G. CANARELLA ET AL..7, and ends n 7:3, as he smoohed probably of low varably decreases o.4. Ths declne s mmedaely followed n 7:4 by a furher sharp decrease o.44. Smlarly, for he UK, he low-volaly regme sars n 99:3, as he smoohed probably rses o.77 and ends n 7: as he smoohed probably of low-varably declnes o.. 5. Conclusons The Grea Moderaon, he sgnfcan declne n he varably of economc acvy, provdes a mos remarkable feaure of he macroeconomc landscape n he las weny years. A number of papers documen he begnnng of he Grea Moderaon n he US and he UK (e.g., [-7]). In hs paper, we use he Markov regmeswchng models of [] and [3] o documen he end of he Grea Moderaon. The analyss uses quarerly raes of growh of real GDP from 957: o 7:4 for he US and from 957: o 7: for he UK. Our resuls place he end of he Grea Moderaon n 7. The Grea Moderaon n he US and he UK begn a dfferen pon n me. In he US he Grea Moderaon sars n 983. In he UK, nsead, begns almos years laer. 5 The explanaons for he Grea Moderaon fall no generally hree dfferen caegores good moneary polcy, mproved nvenory managemen, or good luck. Accordng o [6], a combnaon of good moneary polcy and beer nvenory managemen led o he Grea Moderaon. The end of he Grea Moderaon, however, occurs a approxmaely he same me n boh he US and he UK. The end of he Grea Moderaon may reflec dfferen reasons, and one may conjecure abou reasons for he end. I seems unlkely ha good moneary polcy would 5 Our fndngs on he begnnng of he Grea Moderaon, usng dfferen mehodologes, mach hose repored n []. The mehodology employed by [6], however, canno denfy he end of he Grea Moderaon, excep wh he passage of me. 6 The reasons why he effecs of ol prce shocks dffer so much beween he 97s and he s are consdered by [3], usng daa hrough 5: 4. Accordng o [3] four dfferen facors help o explan he dfferences - (a) good luck (.e., lack of concurren adverse shocks), (b) smaller share of ol n producon, (c) more flexble labor markes, and (d) mprovemens n moneary polcy. (p. ). We noe ha snce 5:4, he ol prce shock worsened dramacally and he housng marke crss n he US and he UK appeared, anoher concurren adverse shock. 7 In hs regard, our fndngs confrm hose of [6], who use a dfferen mehodology. They fnd ha nroducng dummy varables o capure he regme swches n he volaly of real GDP growh elmnaes he GARCH and ARCH processes for he volaly processes n each subperod. Table 8 repors smlar resuls n ha he auoregressve coeffcens n he ARCH () processes n he Markov regme-swchng AR ()-ARCH () model prove nsgnfcanly dfferen from zero. In oher words, a homoskedasc error process exss for he hgh-and lowvolaly regmes. urn no bad polcy or ha beer nvenory managemen would urn no worse managemen. Raher, he lkely explanaon comes from bad luck. Two lkely culprs exs energy prce and housng prce shocks. 6 We leave hs conjecure abou he end of he Grea Moderaon for fuure research as more daa become avalable wh whch o address he queson. Relang drecly o he commens n he pror paragraph, Reference [56] compares he curren sub-prme crss n he US o 8 bank-cenered fnancal crses. Srkng smlares exs beween he curren US suaon and hose of he 8 fnancal crses examned, ncludng he run up and collapse of housng and equy prces, he curren level of he curren accoun defc o GDP, he paern of changes n real GDP per capa growh, and he rse n he publc deb s share of GDP. They also sae ha a smlar suaon exss n he UK. In sum, he US suaon, and he suaon n he UK, provde sunnng quanave and qualave parallels across a number of sandard fnancal crss ndcaors. Besdes he Grea Moderaon ssue, anoher reason exss o nvesgae regme changes n he volaly of economc acvy. The well-known auoregressve condonally heeroskedasc models, based on he semnal work by [] and [], play an mporan role n he esmaon of volales. Problems assocaed wh esmang such models, however, may arse f he underlyng volaly process ncorporaes srucural breaks, especally shfs n he overall level of volaly. 7 In hs paper, we show ha he varance process s (almos) non-saonary. The hgh perssence ha we fnd n sngle-regme models may merely reflec he dsregardng he problem of regme changes (.e., he hgh perssence may smply occur because of a msspecfed model). We fnd perssence. The perssence, however, does no resde n he shocks, bu raher n he regmes. We mus confess n concluson ha we dd no expec our fndng of he possble end o he Grea Moderaon. Tha fndng came as a complee surprse. Is rue? Tme wll ell. Before concludng, we offer some caveas abou our fndng. Frs, he relably of our daa seres probably deeroraes a he end of he sample, where daa revsons may sll occur. Such daa revsons could reverse our fndng. Second, f he Grea Moderaon largely reflecs beer moneary polcy, hen wll no he cenral banks engage n he approprae acons ha wll lead o a false sgnal? Tha s, wll moneary polcy makers neuralze hose facors ha sgnal a reurn o he hgh volaly regme? Thrd, he added worldwde demand comng from Chna, Inda, and oher counres may consue an added dose of bad luck, especally when combned wh he energy and housng marke shocks. In sum, we conclude ha he emprcal evdence sgnals he end of he Grea Moderaon. Noneheless, we sll carry some reservaons abou our fndng. Copyrgh ScRes.

45 G. CANARELLA ET AL References [] R. F. Engle, Auoregressve Condonal Heeroscedascy wh Esmaes of he Varance of Uned Kngdom Inflaon, Economerca, Vol. 5, No. 4, 98, pp [] T. Bollerslev, Generalzed Auoregressve Condonal Heeroskedascy, Journal of Economercs, Vol. 3, No. 3, 986, pp [3] Klaassen, Improvng GARCH Volaly Forecass wh Regme-Swchng GARCH, Emprcal Economcs, Vol. 7, No.,, pp [4] C. G. Lamoureux and W. D. Lasrapes, Perssence n Varance, Srucural Change and he GARCH Model, Journal of Busness and Economc Sascs, Vol. 8, No., 99, pp [5] A. Tmmerman, Momens of Markov Swchng Models, Journal of Economercs, Vol. 96, No.,, pp [6] W. Fang, S. M. Mller and C. Lee, Cross-Counry Evdence on Oupu Growh Volaly: Nonsaonary Varance and GARCH Models, Scosh Journal of Polcal Economy, Vol. 55, No. 4, 8, pp [7] A. Sansó, V. Arragó and J. L. Carron, Tesng for Change n he Uncondonal Varance of Fnancal Tme Seres, Revsa de Economá Fnancera, Vol. 4, No. 4, 4, pp [8] W. Fang and S. M. Mller, The Grea Moderaon and he Relaonshp beween Oupu Growh and s Volaly, Souhern Economc Journal, Vol. 74, No. 3, 8, pp [9] J. D. Hamlon, Raonal-Expecaons Economerc Analyss of Changes n Regme: An Invesgaon of he Term Srucure of Ineres Raes, Journal of Economc Dynamcs and Conrol, Vol., No. -3, 988, pp [] J. D. Hamlon, A New Approach o he Economc Analyss of Nonsaonary Tme Seres and he Busness Cycle, Economerca, Vol. 57, No., 989, pp [] J. Km and C. R. Nelson, Has he U.S. Economy Become More Sable? A Bayesan Approach Based on a Markov-Swchng Model of he Busness Cycle, Revew of Economcs and Sascs, Vol. 8, No. 4, 999, pp [] M. M. McConnell and G. Perez-Quros, Oupu Flucuaons n he Uned Saes: Wha has Changed snce he Early 98 s? Amercan Economc Revew, Vol. 9, No. 5,, pp [3] O. J. Blanchard and J. Galí, The Macroeconomc Effecs of Ol Prce Shocks: Why are he s So Dfferen from he 97s? MIT Deparmen of Economcs Workng Paper No. 7-, 7. [4] O. J. Blanchard and J. Smon, The Long and Large Declne n U. S. Oupu Volaly, Brookngs Papers on Economc Acvy, Vol., No.,, pp [5] T. C. Mlls and P. Wang, Have Oupu Growh Raes Sablzed? Evdence from he G-7 Economes, Scosh Journal of Polcal Economy, Vol. 5, No. 3, 3, pp [6] P. M. Summers, Wha Caused he Grea Moderaon? Some Cross-Counry Evdence, Economc Revew, Federal Reserve Bank of Kansas Cy, 5, pp [7] J. H. Sock and M. W. Wason, Undersandng Changes n Inernaonal Busness Cycle Dynamcs, Journal of he European Economc Assocaon, Vol. 3, No. 5, 5, pp [8] C. Ken, K. Smh and J. Holloway, Declnng Oupu Volaly: Wha Role for Srucural Change? In: C. Ken and D. Norman, Eds., The Changng Naure of he Busness Cycle, Reserve Bank of Ausrala, 5, pp [9] S. G. Cecche, A. Flores-Lagunes and S. Krause, Assessng he Sources of Changes n he Volaly of Real Growh, In: C. Ken and D. Norman, Eds., The Changng Naure of he Busness Cycle, Reserve Bank of Ausrala, 5, pp [] J. H. Sock and M. W. Wason, Has he Busness Cycle Changed? Evdence and Explanaons, Moneary Polcy and Uncerany: Adapng o a Changng Economy, Proceedngs of Symposum sponsored by Federal Reserve Bank of Kansas Cy, Jackson Hole, Wyomng, 3, pp [] S. Ahmed, A. Levn and B. A. Wlson, Recen U.S. Macroeconomc Sably: Good Polces, Good Pracces, or Good Luck? Revew of Economcs and Sascs, Vol. 86, No. 3, 4, pp [] R. Clarda, J. Galí and M. Gerler, Moneary Polcy Rules and Macroeconomc Sably: Evdence and Some Theory, Quarerly Journal of Economcs, Vol. 5, No.,, pp [3] B. S. Bernanke, The Grea Moderaon, Speech a Easern Economc Assocaon, Washngon, February 4. [4] J. H. Sock and M. W. Wason, Has he Busness Cycle Changed and Why? In: M. Gerler and K. Rogoff, Eds., NBER Macroannual, MIT Press, Cambrdge,, pp [5] G. E. Prmcer, Tme Varyng Srucural Vecor Auore- Gressons and Moneary Polcy, Revew of Economc Sudes, Vol. 7, No. 3, 5, pp [6] C. Sms and T. Zha, Were There Regme Swches n U.S. Moneary Polcy? Amercan Economc Revew, Vol. 96, No., 6, pp [7] L. Gambe, E. Pappa and F. Canova, The Srucural Dynamcs of US Oupu and Inflaon: Wha Explans he Changes? Journal of Money, Cred and Bankng, Vol. 4, No. -3, 6, pp [8] T. Lubk and F. Schorfhede, Tesng for Indeermnacy: An Applcaon o U. S. Moneary Polcy, Amercan Economc Revew, Vol. 94, No., 4, pp [9] J. Bovn and M. Gannon, Has Moneary Polcy Become More Effecve? The Revew of Economcs and Sascs, Vol. 88, No. 3, 6, pp [3] L. Bena and P. Surco, VAR Analyss and he Grea Copyrgh ScRes.

46 4 G. CANARELLA ET AL. Moderaon, European Cenral Bank, Workng Paper # 866, February 8. [3] J. D. Hamlon and R. Susmel, Auoregressve Cond- Tonal Heeroskedascy and Changes n Regme, Journal of Economercs, Vol. 64, No. -, 994, pp [3] J. Km, C. R. Nelson and R. Sarz, Tesng for Mean Reverson n Heeroskedasc Daa Based on Gbbs Samplng Augmened Randomzaon, Journal of Emprcal Fnance, Vol. 5, No., 998, pp [33] R. Bhar and S. Hamor, Alernave Characerzaon of he Volaly n he Growh Rae of Real GDP, Japan and he World Economy, Vol. 5, No., 3, pp [34] F. X. Debold, Commens on Modellng he Perssence of Condonal Varance, Economerc Revews, Vol. 5, No., 986, pp [35] R. F. Engle and T. Bollerslev, Modellng he Perssence of Condonal Varance, Economerc Revews, Vol. 5, No., 986, pp. -5. [36] T. Mkosch and C. Sărcă, Non-Saonares n Fnancal Tme Seres, he Long-Range Dependence, and he IGARCH Effecs, Revew of Economcs and Sascs, Vol. 86, No., 4, pp [37] E. Hllebrand, Neglecng Parameer Changes n GARCH Models, Journal of Economercs, Vol. 9, No. -, 5, pp [38] W. Kramer and B. T. Azamo, Srucural Change and Esmaed Perssence n he GARCH(,)-Model, Economcs Leers, Vol. 97, No., 7, pp [39] S. Gray, Modelng he Condonal Dsrbuon of Ineres Raes as a Regme Swchng Process, Journal of Fnancal Economcs, Vol. 4, No., 996, pp [4] M. Sola and A. G. Tmmerman, Fng he Momens: A Comparson of ARCH and Regme-Swchng Models for Daly Sock Reurns, Workng Paper, London Busness School, 994. [4] R. Flecher, A New Approach o Varable Merc Algorhm, Compuer Journal, Vol. 3, No. 3, 97, pp [4] R. B. Daves, Hypohess Tesng when a Nusance Para-Meer s Presen Only under he Alernave, Bomerka, Vol. 74, No., 987, pp [43] Kanas and M. Genus, Regme (Non)Saonary n he US/UK Real Exchange Rae, Economcs Leers, Vol. 87, No. 3, 5, pp [44] L. Ramchand and R. Susmel, Cross Correlaons across Major Inernaonal Markes, Journal of Emprcal Fnance, Vol. 5, No. 4, 998, pp [45] C. G. Broyden, The Convergence of a Class of Double- Rank Mnmzaon Algorhms, IMA Journal of Appled Mahemacs, Vol. 6, No., 97, pp [46] D. Goldfarb, A Famly of Varable Merc Mehods Derved by Varaonal Means, Mahemacal Compuaon, Vol. 4, 97, pp [47] D. F. Shanno, Condonng of Quas-Newon Mehods for Funcon Mnmzaon, Mahemacs of Compuaon, Vol. 4, No., 97, pp [48] E. K. Bernd, B. H. Hall, R. E. Hall and J. A. Hausmann, Esmaon and Inference n Nonlnear Srucural Models, Annals of Economc and Socal Measuremen, Vol. 3, No. 4, 974, pp [49] D. Brunner, Condonal Asymmeres n Real GDP: A Semparamerc Approach, Journal of Busness and Economc Sascs, Vol., No., 99, pp [5] D. Brunner, On he Dynamc Properes of Asymmerc Models of Real GDP, The Revew of Economcs and Sascs, Vol. 79, No., 997, pp [5] M. V. French and D. Schel, Cyclcal Paerns n he Varance of Economc Acvy, Journal of Busness and Economc Sascs, Vol., No., 993, pp [5] B. E. Hansen, The Lkelhood Rao Tes Under Nonsandard Condons: Tesng he Markov Swchng Model of GNP, Journal of Appled Economercs, Vol. 7, 99, pp. S6-S8. [53] R. Garca, Asympoc Null Dsrbuon of he Lkelhood Rao Tes n Markov Swchng Models, Inernaonal Economc Revew, Vol. 39, No. 3, 998, pp [54] M. Lu, Modellng Long Memory n Sock Marke Volaly, Journal of Economercs, Vol. 99, No.,, pp [55] C. S. Wong and W. K. L, On a Mxure Auoregressve Condonal Heeroskedasc Model, Journal of he Amercan Sascal Assocaon, Vol. 96, No. 455,, pp [56] C. M. Renhar and K. S. Rogoff, Is he 7 US Sub- Prme Fnancal Crss So Dfferen? An Inernaonal Hsorcal Comparson, Amercan Economc Revew: Papers and Proceedngs, Vol. 98, No., 8, pp Copyrgh ScRes.

47 Modern Economy,,, do:.436/me..3 Publshed Onlne May (hp:// Prce-Seng Mxed Duopoly Models wh Complemenary Goods Absrac Kazuhro Ohnsh Insue for Basc Economc Scence, Osaka, Japan E-mal: Receved March 4, ; revsed March 5, ; acceped Aprl 5, Ths paper consders domesc (resp. nernaonal) Berrand mxed duopoly compeon n whch a saeowned welfare-maxmzng publc frm and a domesc (resp. foregn) prof-maxmzng prvae frm produce complemenary goods. The man purpose of he paper s o presen and o compare he equlbrum oucomes of he wo mxed duopoly models. Keywords: Complemenary Goods, Prce Compeon, Domesc Mxed Duopoly, Inernaonal Mxed Duopoly. Inroducon The analyss of mxed marke models ha ncorporae sae-owned welfare-maxmzng publc frms has receved consderable aenon n recen years and has been wdely performed by many researchers. However, mos sudes consder quany compeon, such as [-6]. Some sudes consder mxed markes wh prce compeon, such as [-6]. These sudes examne prceseng mxed marke models wh domesc frms and do no nclude foregn frms. Ohnsh [7] consders an nernaonal mxed marke n whch a sae-owned publc frm compees on prce wh a foregn prvae frm. However, hs sudy examnes mxed duopoly compeon n whch publc and foregn prvae frms produce mperfecly subsuable goods. To he bes of my knowledge, he analyss of nernaonal Berrand mxed markes wh publc and foregn prvae frms producng complemenary goods has been gnored. Therefore, we analyze he behavor of a sae-owned publc frm and a foregn prvae frm n an nernaonal prce-seng model wh complemenary goods. We consder boh domesc and nernaonal mxed duopoly models wh complemenary goods. The man purpose of hs paper s o presen and o compare he equlbrum oucomes of he wo mxed duopoly models. The remander of he paper proceeds as follows. In Secon, we formulae a domesc Berrand mxed duopoly model n whch a sae-owned publc frm and a domesc prvae frm produce complemenary goods. We See, for example, [7-] for excellen surveys. show he slope of each frm s reacon curve n he domesc Berrand mxed duopoly model wh complemenary goods. We presen he equlbrum oucome of he domesc Berrand mxed duopoly model wh complemenary goods. Secon 3 analyzes he equlbrum oucome of an nernaonal Berrand model n whch a sae-owned publc frm and a foregn prvae frm produce complemenary goods. Secon 4 compares he equlbrum oucomes of he wo mxed duopoly models. Fnally, Secon 5 concludes he paper.. Domesc Mxed Duopoly wh Complemenary Goods In hs secon, we consder a marke n whch one saeowned welfare-maxmzng publc frm and one domesc prof-maxmzng prvae frm produce complemenary goods. The basc srucure s from Bárcena-Ruz [5]. In he remander of hs paper, subscrps S and D denoe he sae-owned frm and he domesc prvae frm, respecvely. There s no possbly of enry or ex. On he consumpon sde, here s a connuum of consumers of he same ype whose uly funcon s lnear. The represenave consumer maxmzes UqS, qd psqs pdqd, where q s he amoun of good and p s s prce S,D. The funcon UqS,qD s quadrac, srcly concave and symmerc n q and : U q, q S qd qs qsqd qd S q a q, where a. The de- D S D Copyrgh ScRes.

48 44 K. OHNISHI mand funcon s gven by 3ap pj q, j S,D; j 3 Each frm s prof funcon s gven by p cq S,D D. (), () where c s he oal cos for each un of oupu. We assume c a o assure ha he producon levels of frms are posve. Domesc socal welfare, whch s he sum of consumer surplus (CS) and profs, s gven by W CS. (3) S From () and (3), we derve he followng reacon funcons n prces: 3c pd RS, (4) 3ac ps RD. (5) 4 From (4) and (5), we can sae he followng: Lemma. In he domesc Berrand mxed marke wh complemenary goods, each frm s reacon funcon s downward slopng. From (4) and (5), he equlbrum can be derved as follows: c 3a ps, (6) 7 6a c pd, (7) 7 q ac, (8) q S 8 D a c. (9) 7 Furhermore, he profs and consumer surplus can be expressed as follows: 6acca S, () 7 a c 48 D, () 49 37a c CS. () 49 From (), we see ha he sae-owned frm s prof s negave. Subsung (), () and () no (3), socal welfare s obaned as 43a c W. (3) 49 From () and (3), we see ha hough he sae-owned frm s prof s negave, socal welfare s hgher han consumer surplus. 3. Inernaonal Mxed Duopoly wh Complemenary Goods In hs secon, we consder a marke n whch one saeowned welfare-maxmzng publc frm and one foregn prof-maxmzng prvae frm produce complemenary goods. In he remander of hs paper, subscrp F denoes he foregn prvae frm. The uly, demand, and prof funcons are he same as hose of he prevous secon. Domesc socal welfare, whch s he sum of consumer surplus and he sae-owned frm s prof, s gven by W CS S. (4) From () and (4), we derve he followng bes response: RS c, (5) 3ac ps RF. (6) 4 From (5), we can sae he followng: Lemma. In he nernaonal Berrand mxed marke wh complemenary goods, he slope of he sae-owned frm s reacon curve s zero. I s shown n Ohnsh [7] ha he slope of he sae-owned frm s reacon curve s zero n nernaonal Berrand mxed duopoly compeon wh mperfec subsuable goods. From (5), we see ha he resul of nernaonal Berrand mxed duopoly compeon wh complemenary goods s smlar o ha of nernaonal Berrand mxed duopoly compeon wh mperfec subsuable goods. From (5) and (6), he equlbrum can be derved as follows: ps c, (7) 3a c pf, (8) 4 3a c qs, (9) qf a c. () From (7), we know ha he sae-owned frm produces an oupu such ha prce equals margnal cos. From (9) and (), we see ha he sae-owned frm s oupu s hgher han he foregn prvae frm s oupu. Furhermore, he profs, consumer surplus, and socal welfare can be expressed as follows: S, () a c 3 F, () 4 Copyrgh ScRes.

49 K. OHNISHI 45 7a c CS, (3) 8 7a c W. (4) 8 We see ha snce he sae-owned frm s prof s zero, socal welfare s equal o consumer surplus. 4. Comparsons In hs secon, we begn by presenng comparave sacs resuls. In he remander of hs paper, superscrps H and I denoe he domesc and nernaonal mxed duopoles, respecvely. We have he followng resuls. p a H S p a I S,, p a H D p a I F,, q a H S q a I S,, q a q a H D I F,. In each model, a rse n a rases he prvae frm s prce. However, n he domesc mxed duopoly model, a rse n a lowers he sae-owned frm s prce, and n he nernaonal mxed duopoly model, a rse n a has no nfluence on he sae-owned frm s prce. Furhermore, we have p c H S, p c H D, q c H S, q c H D, I I I I ps p, F q S q,, F. c c c c A rse n c rases he frms prces and decreases her oupus. We see ha he comparave sacs resuls are almos he same n boh models. We now compare he equlbrum oucomes of he wo models. The man resul of hs sudy s descrbed by he followng proposon. Proposon. In he equlbrum oucomes of he domesc and nernaonal mxed duopoly models, ) H I H I H I H I S S; ) D F ; 3) CS CS ; and 4) W W. I Proof. ) From (), we see ha. Furhermore, S H from () and c a, S s negave. H ) From (), () and c a, boh D and I F are posve, and hus H 48 D ac 49 9 I 3 47 ac F ac ac The proofs of 3) and 4) are omed, snce hey are he same as he proof of ). Q.E.D. Proposon saes ha consumer surplus s hgher n he nernaonal mxed duopoly equlbrum han n he domesc mxed duopoly equlbrum. 5. Conclusons We have frs consdered a domesc Berrand model n whch a sae-owned welfare-maxmzng publc frm and a domesc prof-maxmzng prvae frm produce complemenary goods. We have shown ha each frm s reacon funcon s downward slopng n domesc Berrand mxed duopoly compeon wh complemenary goods. In addon, we have found ha he sae-owned frm s prof s negave n equlbrum. Second, we have consdered an nernaonal Berrand model n whch a sae-owned publc frm and a foregn prvae frm produce complemenary goods. We have hen shown ha he slope of he sae-owned frm s reacon curve s zero, and so socal welfare s equal o consumer surplus. Thrd, we have compared he equlbrum oucomes of he wo mxed models. We have demonsraed ha hough he sae-owned frm s prof, he prvae frm s prof, and socal welfare are hgher n he domesc mxed duopoly equlbrum han n he nernaonal mxed duopoly equlbrum, consumer surplus assocaed wh he nernaonal mxed duopoly equlbrum exceeds consumer surplus assocaed wh he domesc mxed duopoly equlbrum. 6. References [] F. Delbono and G. Rossn, Compeon Polcy vs Horzonal Merger wh Publc, Enrepreneural, and Labor- Managed Frms, Journal of Comparave Economcs, Vol. 6, No., June 99, pp [] F. Delbono and V. Dencolò, Regulang Innovave Acvy: The Role of Publc Frm, Inernaonal Journal of Indusral Organzaon, Vol., No., March 993, pp [3] L. Ne, Why Prvae Frms are More Innovave han Publc Frms, European Journal of Polcal Economy, Vol., No. 4, December 994, pp [4] J. Wllner, Welfare Maxmzaon wh Endogenous Average Coss, Inernaonal Journal of Indusral Organzaon, Vol., No. 3, Sepember 994, pp [5] K. Fjell and D. Pal, A Mxed Olgopoly n he Presence of Foregn Prvae Frms, Canadan Journal of Economcs, Vol. 9, No. 3, Augus 996, pp [6] K. George and M. La Manna, Mxed Duopoly, Ineffcency, and Publc Ownershp, Revew of Indusral Organzaon, Vol., No. 6, December 996, pp [7] M. D. Whe, Mxed Olgopoly, Prvazaon and Subsdzaon, Economcs Leers, Vol. 53, No., November Copyrgh ScRes.

50 46 K. OHNISHI 996, pp [8] S. Mujumdar and D. Pal, Effecs of Indrec Taxaon n a Mxed Olgopoly, Economcs Leers, Vol. 58, No., February 998, pp [9] D. Pal, Endogenous Tmng n a Mxed Olgopoly, Economcs Leers, Vol. 6, No., November 998, pp [] D. Pal and M. D. Whe, Mxed Olgopoly, Prvazaon, and Sraegc Trade Polcy, Souhern Economc Journal, Vol. 65, No., Aprl 998, pp [] J. Poyago-Theooky, R&D Compeon n a Mxed Duopoly Under Uncerany and Easy Imaon, Journal of Comparave Economcs, Vol. 6, No. 3, Sepember 998, pp [] K. Fjell and J. S. Heywood, Publc Sackelberg Leadershp n a Mxed Olgopoly wh Foregn Frms, Ausralan Economc Papers, Vol. 4, No. 3, Sepember, pp [3] T. Masumura, Sackelberg Mxed Duopoly wh a Foregn Compeor, Bullen of Economc Research, Vol. 55, No. 3, July 3, pp [4] L. Han and H. Ogawa, Economc Inegraon and Sraegc Prvazaon n an Inernaonal Mxed Olgopoly, FnanzArchv, Vol. 64, No. 3, Sepember 8, pp [5] K. Ohnsh, Inernaonal Mxed Duopoly and Sraegc Commmens, Inernaonal Economcs and Economc Polcy, Vol. 4, No. 4, February 8, pp [6] J. Fernández-Ruz, Manageral Delegaon n a Mxed Duopoly wh a Foregn Compeor, Economcs Bullen, Vol. 9, No., February 9, pp [7] D. Bös, Publc Enerprse Economcs, Norh-Holland, 986. [8] D. Bös, Prvazaon: A Theorecal Treamen, Clarendon Press,. [9] J. Vckers and G. Yarrow, Prvazaon: An Economc Analyss, MIT Press, 988. [] H. Cremer, M. Marchand and J.-F. Thsse, The Publc Frm as an Insrumen for Regulang an Olgopolsc Marke, Oxford Economc Papers, Vol. 4, No., January 989, pp [] L. Ne, Mxed Olgopoly wh Homogeneous Goods, Annals of Publc and Cooperave Economcs, Vol. 64, No. 3, July 993, pp [] D. Bös, Income Taxaon, Publc Secor Prcng and Redsrbuon, Scandnavan Journal of Economcs, Vol. 86, No., June 984, pp [3] H. Cremer, M. Marchand and J.-F. Thsse, Mxed Olgopoly wh Dfferenaed Producs, Inernaonal Journal of Indusral Organzaon, Vol. 9, No., March 99, pp [4] A. Ogawa and K. Kao, Prce Compeon n a Mxed Duopoly, Economcs Bullen, Vol., No. 4, July 6, pp. -5. [5] J. C. Bárcena-Ruz, Endogenous Tmng n a Mxed Duopoly: Prce Compeon, Journal of Economcs, Vol. 9, No. 3, July 7, pp [6] J. C. Barcena-Ruz and M. B. Garzón, Capacy Choce n a Mxed Duopoly under Prce Compeon, Economcs Bullen, Vol., No. 6, Ocober 7, pp. -7. [7] K. Ohnsh, Domesc and Inernaonal Mxed Models wh Prce Compeon, Inernaonal Revew of Economcs, Vol. 57, No., March, pp. -7. Copyrgh ScRes.

51 Modern Economy,,, 47-5 do:.436/me..4 Publshed Onlne May (hp:// Is Raonal o Mnmze Tax Paymens? Absrac Andreas Löffler, Luz Kruschwz Unversä Paderborn, Lehrsuhl für Fnanzerung und Inveson, Paderborn, Germany Free Unversä Berln, Insu für Bank-und Fnanzwrschaf, Berln, Germany E-mal: AL@wacc.de, LK@wacc.de Receved March 5, ; revsed Aprl 5, ; acceped Aprl 5, The opnon s occasonally voced ha nvesors should avod payng ax a all coss. In hs paper s beng nvesgaed, usng a smple porfolo model wh axes, wheher avodng ax really leads o more µ-σ-effcen soluons. I s demonsraed for four dfferen conceps of ax-mnmsng polcy ha hey are a far cry from an effcen soluon. Keywords: Decson, Taxes, CAPM, Tax-CAPM. Problem Oulne Consderng he queson on how o ncrease one s ne ncome, an nvesor has wo opons. He or she wll eher look for opporunes o ncrease he pre-ax ncome, or alernavely o dmnsh ax paymens. Many people are assumed o especally favor ax savng schemes. A few years ago, a German economs, Ekkehard Wenger, has wren on hs predlecon, whch he consders horoughly reasonable. Raonally acng nvesors would eher make legal use of ax ncenves n her nvesmens, or even aemp ax evason. Anyone acng dfferenly would be maxmzng supdy []. Regardless of wheher one agrees or no wh such drasc vews, he raonale behnd such a poson seems o make sense. As a scens however, one should be armed wh a fundamenally skepcal oulook; easly comprehended maers do no always f n wh realy, as one readly learns n school from he conundrum nvolvng Achlles and he urle. Wenger s consderaons are relevan n vew of emprcal analyses of he sock marke. Far evaluaons of companes values are normally performed by usng Capal Asse Prcng Models (CAPM). Ths nvolves he comparson wh smlar companes, n order o deermne he so-called bea facor of he frm n queson. Parcularly he fnancal audor professon s adaman ha for hs deermnaon no he basc model of CAPM be used, bu raher s ax-enabled verson, he Tax- CAPM []. The values resulng from he respecve uses of CAPM and Tax-CAPM can somemes vary sgnfcanly. If one subscrbes o he opnon ha ax paymens reflec rraonal behavor, follows ha Tax-CAPM wll yeld ncorrec company valuaons. Thus, he queson of wheher savng axes consues raonal behavor, drecly affecs wha a company s worh. In our presen conrbuon we wll, whle usng he framework of porfolo heory, examne wheher a polcy of mnmzng axes can be regarded as advanageous. For hs purpose, we consder a smple porfolo problem from a ax perspecve and aemp a characerzaon of all porfolos whch are effcen under uncerany. Such porfolos can be characerzed as desrable even whou more precse knowledge on he rsk averseness of nvesors. On hs bass we wll examne he queson, how he concep of ax mnmzaon can be formalzed n our conex and f such conceps can be effcen. I wll emerge ha ax mnmzers, whle maybe consderng hemselves o be parcularly clever, end up lookng less han smar. We wll concenrae our analyss exclusvely on porfolo heory and wll no employ he CAPM. Ths procedure follows from he goal we have se for ourselves. We would lke o show ha even raonal nvesors can be wllng payers of axes, as hey prefer a balanced aferax srucure of paymens. Wha knd of macroeconomc resul would be he upsho of such behavor s ousde he scope of our work.. The Model We use a formal model whch s based on defnons and smplfyng assumpons deemed approprae. On hs bass we wll use logcal operaons o draw conclusons whose valdy can be checked by an exper hrd person a any me. Gven ha we do no make msakes durng Copyrgh ScRes.

52 48 A. LÖFFLER ET AL. he logcal operaons, our resuls can only be legmaely crcsed by referrng o a possble use of napproprae assumpons... Assumpons We are lookng a a one perod model under uncerany. An nvesor has he opon o nves n rsky secures j,, J. The prce vecor of hese nvesmens s called p p,, pj. We noae fuure paymens conneced wh he secures wh Y j. We use he symbol E EY,, E Y J for he vecor of he expeced cashflows. The covarance marx of he cashflows s. I s assumed ha he covarance marx s regular. Therefore here are no redundan nvesmens. A rsk free asse wll no be nroduced. Bu we concenrae on he edge of an eggshell-lke surface whch may be nerpreed as he geomerc place of all desrable rsk-reurn-posons and uses o be called he effcen se. We mply an nvesor wh nomnal asses of, who has already fnanced hs momenary consumpon and has o decde how o nves he amoun n he capal marke. For ha purpose he chooses a porfolo conssng of N N,, N J uns of he rsky asses. Shor sellng s no excluded. Therefore some enres n hs vecor may also be negave. When decdng on hs nvesmen he nvesor orens hmself by he expecaon value and varance. He hus has a uly funcon of he ype U,. Accordng o our requremens he expecaon value and varance of he fuure paymens of a secures porfolo are deermned o N E and NN. The prce of he porfolo s gven by he vecor produc N p. In order o model he axaon an assessmen bass as well as a ax-rae funcon s requred. As assessmen bass for a un of he j -h fnancal asse we us he dfference beween he rsky cashflow and a rskless deprecaon whch n he smples case corresponds o he purchase prce, bu no necessarly. We erm he vecor of he deprecaons of he rsky asses as A A,, AJ. The rae funcon s lnear, he ax rae s secure... Effcen Porfolos before and afer Taxes Frs we look a he decson under he smplfyng assumpon ha no axes are beng leved. Then we deal wh he classc problem of porfolo selecon, nroduced no he leraure by Markowz more han 5 years ago [3]. The nvesor can choose beween posons chared on an - -dagram lad ou on an eggshell-shaped surface. The mos neresng pons on hs surface are hose around he edge, as s here ha for any gven expeced wealh he varance wll be mnmal. All posons whch are no suaed on he edge are denoed as non-effcen. Any raonal nvesor wll aemp o occupy an - - effcen poson. In order o deermne hese edge posons, a maxmzaon problem max N E () N under budge consrans and () N p N N has o be solved. The frs condon s a budge resrcon whch ensures ha he nvesor s wealh s fully exhaused; he second condon makes sure ha he cash flow varance of a porfolo wll reach an exogenously demanded level. In order o fully deermne he effcen se, he opmzaon problem has o be solved for all possble. Because shor sales are no excluded, he opmzaon can be accomplshed by usng a Lagrange funcon. The specfc soluon s rrelevan o hs dscusson. We now focus our aenon on afer-ax-effcen porfolos. Here, when dealng wh cash flows, we mus noe ha axes are due. An nvesor holdng one un of asse j wll have o delver he amoun Y j Aj o he ax auhory. Effcen porfolos are hose, whch for any gven varance and nomnal wealh, wll maxmze he expeced value e. The expeced cash flows afer axes hen amoun o E E A EA. The pre-ax covarance marx changes o he pos-ax covarance marx A Y Cov Y j j, k A k Cov Y j, Y k Thus, we now have o maxmze he funcon N E A under he budge consrans N p and N N. So long as he amoun of wre-offs A s no specfed, here are many soluons o hs problem. However, n a one-perod model, A p represens a plausble-even nauralchoce. The funcon o be maxmzed now akes he If cash flows are no perfecly negavely correlaed here are no porfolos havng zero varance. Therefore, here s a mnmum varance ha canno be undercu. Copyrgh ScRes.

53 A. LÖFFLER ET AL. 49 form NE. Snce a posve lnear ransformaon wll affec he arge funcon bu no he soluon self, we can smlarly denoe he opmzaon problem afer axes n he form maxn N E (3) under auxlary condons N p and NN (4) We recognze a once: The maxmzaon problem afer axes dffers from ha before axes n only one, and furhermore rrelevan, respec. In he second budge con- sran, became he parameer. I follows ha he se of all parameers for boh maxmzaon problems mus be dencal. The effcen se before axes concdes wh he effcen se afer axes..3. Tax-Mnmzng Porfolos We begn by sang ha, n he conex of our dscusson, s no mmedaely clear wha ax avodance or ax mnmzaon mean. We see several possble ways o specfy he concep of ax mnmzaon, f we are dealng wh denfyng a rsky porfolo. Four specfc alernaves shall be consdered. In each case, we wll assume ha he rsky projecs wll be compleely wren off, hus A p..3.. Mnmzng Taxes n he Wors-Case Scenaro To formalze hs concep of ax mnmzaon, we assume ha he number of relevan saes a me s fne and ha he sae-dependen cash flows of asses can be characerzed by Ys, s,, S. Then NYs pn Ys descrbes he ax paymens comng due for an nvesor f he sae s occurs n. In he wors case, hs paymen wll amoun o max s NYs. Our frs verson of ax mnmzaon may amoun o choosng porfolo N n such a manner, as o mnmze he hghes ax amoun possble mn max N Y N s s under auxlary consran N p. The soluon can be found by means of an approprae algorhm of lnear programmng. I s obvous ha such a soluon s no - -effcen..3.. Absolue Mnmzaon of Expeced Taxes The expeced ax paymens of porfolo N amoun o NE p. Due o he budge resrcon N p, he opmzaon problem reads mn NE, N f no addonal auxlary condons are aken no accoun. The soluon s no lower-bound. The expeced ax paymen ends owards nfne mnus. Ths resul does no make economc sense Fadng Expeced Taxes In order o avod he jus menoned oucome, we can resrc he search for a porfolo, for whch he expeced ax paymens dsappear,.e., N E!. For a posve ax rae, he expeced ax paymen wll end owards zero f he bass of assessmen dsappears. Ths s he case, f he expeced paymens from he porfolo are equal o he nvesed capal, a slghly surprsng, bu equally dsapponng oucome. Whou earnng no axes are due. Bu would someone cancel one's ne earnngs n order o save axes? Ths would be as unreasonable as f a frm maxmzed s wages n order o mnmze corporae axes Mnmzng Expeced Taxes on a Gven Varance As a fnal verson of a ax-mnmzng polcy, we consder under he consrans mn NE N N p and NN hs verson of ax mnmzaon we do no have any economcs-drven nuon, excludng maybe ha he deermnaon of an effcen porfolo whou akng varance no accoun does no seem possble. As he consans n he arge funcon can be gnored, we can rewre n he form mn N N E. Comparng hs opmzaon problem wh he procedure nvolvng Equaons () and (), becomes mmedaely clear, ha no - -effcen porfolos can be deermned n hs manner. A raonal nvesor does no mnmze he expeced axes a a gven varance. He or she wll nsead maxmze hem. 3. Conclusons In he framework of a smple porfolo model wh axes was consdered wheher he sraegy of ax avodance wll lead o - -effcen soluons. The examnaon Copyrgh ScRes.

54 5 A. LÖFFLER ET AL. of four dsnc conceps of ax mnmzaon sraegy has proven ha each of hem (by far) msses an effcen soluon. Thus, when evaluang companes, one mus avod he classc CAPM for deermnng bea facors and should nsead employ a Tax-CAPM. 4. References [] E. Wenger, Verznsungsparameer n der Unernehmensbewerung: Berachungen aus heorescher und emprscher Sch, n German, De Akengesellschaf, Vol. 5, 5, pp. 9-. [] M. Jonas, A. Löffler and J. Wese, Das CAPM m deuscher Enkommenseuer, n German, De Wrschafsprüfung, Vol. 57, No. 7, 4, pp [3] H. M. Markowz, Porfolo Selecon, The Journal of Fnance, Vol. 7, No., 95, pp Copyrgh ScRes.

55 Modern Economy,,, 5-58 do:.436/me..5 Publshed Onlne May (hp:// Drec Mechansms, Menus and Laen Conracs Absrac Gwenaël Paser, IPAG Busness School, Pars, France Luxembourg School of Fnance, Luxembourg, Luxembourg E-mal: Receved February 7, ; revsed March, ; acceped March 3, In common agency games, one canno characerze all equlbra by consderng only drec mechansms. In an aemp o overcome hs dffculy, Peers [] and Marmor and Sole [] denfed a class of ndrec mechansms (namely, menus) whch are able o characerze every equlbrum. Unforunaely, menus are dffcul o handle, and several mehodologes have been proposed n he leraure. Here, s shown ha, even f auhors consder menus raher han smpler mechansms, many equlbra descrbed n he leraure could have been characerzed by drec ncenve compable mechansms. Use of more sophscaed mechansms was no necessary n hese cases. Keywords: Common Agency, Revelaon Prncple, Delegaon Prncple, Drec Mechansms, Menus, Laen Conracs. Inroducon The resrcon o drec ncenve compable mechansms s a cornersone of conrac heory. I provdes a smple and elegan mehod for characerzng arbrary equlbra n any prncpal-agen model, even wh very complex communcaon beween he players. Because of s racably, he prncpal-agen model has been very successful, and has revalzed many economc felds: Regulaon, redsrbuon, nsurance and ohers. Mulagen games have provded he bass for aucon heory and he heory of he provson of publc goods. Unforunaely, he resrcon o drec ncenve compable mechansms causes some loss of generaly n mul-prncpal games. Inuvely, smple conracs fal o be general because he srucure of he game nvolves endogenous nformaon. For a prncpal, relevan nformaon ncludes no only he ype of he agen (for example hs/her wllngness o pay n a case of a duopoly) bu also he message ha he agen sends o oher prncpals; he message sen ses a parcular agreemen beween a prncpal and he agen, whch could modfy he agen s wllngness o pay for he producs of oher prncpals. A sraegy for overcomng hs lmaon s o gve up he concep of drec mechansm or any of s generalzaons, and consder he Taxaon Prncple. Ths prncple was nroduced by Hammond [4], Guesnere [5] See Laffon and Marmor [3] for a complee survey. and Roche [6], and saes ha here s no loss of generaly n consderng menus, or nonlnear prces. Peers [] and Marmor and Sole [] show ha an equvalen of he Taxaon Prncple (hey call Delegaon Prncple) makes possble o characerze any equlbrum of any common agency game. The problem wh hs approach s ha he concep of menu s large for common agency games, and, even f smplfes he game, equlbra reman hard o characerze. To reach racable problems, oher ad hoc assumpons are added o resrc he menu se. The presen paper does no queson he valdy of he dfferng furher assumpons made n he leraure. We welcome assumpons (dfferenably or connuy) f hey allow ready characerzaon of equlbra n hs class of games. The cos of hese assumpons s probably a loss of generaly. Neverheless, he auhor does no beleve ha resrcons nvaldae he resuls obaned wh menus. The mehodologes used o fnd a fxed-pon n common agency games n whch menus are allowed are crczed. The presen paper shows ha, n almos all models of he common agency leraure, equlbra characerzed by menus could have been characerzed by drec mechansms. The basc nuon s ha menus can characerze a large se of equlbra because a prncpal, by usng a menu, can creae sophscaed rewards. In common agency games, some equlbra may be susaned by dsconnuous menus; see Laffon and Trole [7] chap. 7. Copyrgh ScRes.