The inflation risk premium on government debt in an overlapping generations model

Transcription

1 The fla pemum geme de a elappg geea mdel Mhael Hahe Depame f m Adam Smh Bue Shl Ue f Glagw Glagw G 8QQ F daf: Augu 0 Th e: Jul 04 Aa A elappg geea mdel wh lg u fla ad a ah--adae a ued dee a ed-de auae led-fm lu f he fla pemum lg-em geme de. The mdel ped ha he fla pemum deped uall he elae mpae f mal d ad apal a ue f eeme ump. I a alaed mdel he peded pemum -al ude plaule leel f ae. The ah--adae a ual f h eul. Kewd: geme de; fla pemum; elappg geea. Idu The fla pemum he mpea demaded -aee mal dhlde f eag fla f lea paal mpae. F ae he que f whehe pmal ue deed geme de wll deped pa he f fag de epame. Ohe hg eg equal a pe fla pemum mple ha geme uld w me heapl ug de ha deed he pe leel. Th aeg wuld eale he geme fae me pedg f a ge pah f ae eep pedg uhaged eal em whle pemael lweg ae. Nehe f hee effe lel e al. Mee a Beae 004 e emae f he fla pemum eale plmae mae feee au fla epea ug ea-ee fla ae he dffeee ewee mal ad deed eld d f he ame mau. Hee he fla pemum mae. I a ee ue Beae ad Wag 00 e ha m empal emae f fla pema ae ul pe wh me ee emae eg a lage a 00 a p. T ee udead he em fa ha de fla pema eeal ee pape hae mpued fla -pema -lea New Keea mdel Adeae 0; De Pal e al. 00; Hödahl e al. 008; Raea ad Seppälä 007. Beaue mal pe ae hee mdel mea pl ha eal effe. A a eul he fla pemum he aae ewee he ha du fa ad fla deped uall he h ha h he em ad he wa ha mea pl epd hee h. F eample ug a adad New Keea mdel De Pal e al. 00 fd ha he g f he fla pemum deped uall whehe he em dmaed pdu mea pl h: pe a wld dmaed pdu h u egae whe mea pl h dmae. Me eel Adeae 0 emae a medum-ale New Keea mdel

2 f he UK em ha allw f me-ag d pema. He lude ha hee wa a uaal fall mal em pema he 990 aued a fall fla pema ha wa de pefeee eme ad fed h ad a me aggee epe fla he Ba f glad. Th heeal leaue ha mped u udeadg f he fa ha de fla pema u he aalale ude ae fed h ad medum-em maue. Th pape am fll h gap udg lg-em fla pema a geeal equlum mdel wh lg u fla. Thee ae eeal gd ea e eeed lgem maue uh a 0-0 ea. F lg-em geme de pla a mpa le ma deelped eme ad au f a -al hae f al maeale geme de. Sed he aalale empal edee ugge ha he fla pemum lg-em geme de mewha hghe ha ha h-em de Hauh e al. 008; Rehee 004. Thd lg-em mal ee ae mae f he am meham f mea pl ag u he mpa f mea pl lg ae a mpa a f eeahe ad plmae. Amg he hg h eque a udeadg f whh fa mae f fla pema ad wh. Th pape mae w u ha mpe f udeadg f lg-em fla pema. F a elappg geea mdel wh lg u fla ad a ah-adae a ued dee a ed-de-auae led-fm lu f he fla pemum lg-em geme de. 4 The mdel ped ha he pemum deped uall he elae mpae f mal d ad apal a ue f eeme ump. Th fdg ha ue appeal e we wuld epe mpea f fla deped he ee whh huehld ae eped uapaed fla hugh mal ae hldg. I a emal pape Depe ad Shede 006 hw ha he pwa ped he US em ha ee que eped uh fluua: a mdeae epde f uapaed fla mple a uaal wealh l f ld age he ma dhlde he em. 5 Lewe he ld Caada le u gfal dug ped f uapaed fla wg pa he uaal hldg f mal geme de Meh ad Teama 0; Meh e al. 00. The mdel peeed hee e wh he ld eg h uapaed fla eaue a adad elappg geea mdel he p f Champ ad Feema 990 ad Hahe 04 whee he ug ae f he ld age whe he ae eed hldg pe amu f mall-demaed geme de. De Pal e al. 00 ep umeal eul f -quae d l; Adeae 0 ad Raea ad Seppälä 007 ep eul f 5-ea ad 0-ea d ad Hödahl e al. 008 ep eul f maue agg fm quae up 0 ea. F eample d wh maue eeedg 5 ea aeaged aud e-hd f uadg UK maeale de e he ped I Caada 0-ea d aued f aud e-ffh f uadg maeale de 008 ad a aeage hae f aud 5% e he ped Daa ue: Hal Daa De Maageme Offe UK; Depame f Fae Caada 0. Rehee 004 de emae he fla pemum del u he fd ha UK wg uld e edued gfal ug medum ad lg-em fla-deed d. 4 Beaue he lu ed-de auae he fla pemum a e me. 5 F ae aed 989 daa a full uapaed fla f 5% ha la 0 ea pdue a wealh l elae aeage e wh f 7% f he age gup ad 0% f he e 75.

3 The ed u hw ha he quaae fla pemum peded he mdel -al ude plaule ala f ae. I paula he mdel ge a aualzed fla pemum f aud 0 a p ude he aele ala. Th ume f he ame de f magude a m empal emae f fla pema ad fal u e aal. B mpa he New Keea leaue dued ae ha uggled geeae zeale fla pema ude adad ala f ae. F ae Raea ad Seppälä 007 Hödahl e al. 008 ad De Pal 00 all fd ha pal alaed New Keea mdel wh eeal ha fma ped fla pema f le ha 0 a p. 6 B a Adeae 0 fd a aeage fla pemum 5-ea d f aud 50 a p a emaed New Keea mdel f he UK em u h fgue ele uall hgh ae hugh pe-z pefeee. Regadg empal ude hee a lage ee leaue whh emae -aage affe mdel f he em uue ad fue mal 5-ea ad 0-ea d maue. 7 The m le fm h leaue ha he aeage fla pemum he u Aea que mde a aud 0 a p e.g. Hödahl ad Ta 0 u h he US ad UK appea hae uaal aeage fla pema wh he m lel age eg a p he UK Adeae 0; Je e al. 00 ad 50 0 a p he US e.g. Ag e al. 008; Che ad Muelle 0. A addal fdg ha he ah--adae a ual f pdug a zeale fla pemum. Th f w ea. F mple ha fla pel elaed me uppl gwh u eel elaed eeme ump. A a eul he ha du fa ad fla ae me gl elaed ha he aee f he ah--adae me. Sed he ah--adae a mple ha fla deped h pdu ad mea lal wheea l mea lal mae whe he ah--adae me ae. Cequel fla e ude ah--adae ad puhe up he fla pemum. The emade f he pape peed a fllw. Se e u he mdel. I Se a led-fm aalal lu f he fla pemum deed ad dued. Se 4 mpae he peded fla pemum wh emae he heeal ad empal leaue. Se 5 egae ue. Fall Se 6 lude.. Mdel The mdel a e f Damd 965 mdel whee he ug ae f ld age ug geme d ad apal. 8 I a hee e: a huehld e a geme e ad a fm e deed he pdu f a gle upu gd. Thee e ae dued h e alg wh he mdel equlum d. 6 Raea ad Seppälä 007 ep egae fla pema. De Pal e al. 00 fd ha he fla pemum a e pe egae depedg h mp. I Hödahl e al. 008 he fla pemum pe e a wde age f maue u de eeed a p. 7 F a eew ee Beae ad Wag 00. A ef eew al pded Se 4. f he pee pape. 8 Damd 965 ude a eal em whee ume hld deed geme de ad apal.

4 . Cume Cde a w-ped elappg geea mdel mla p Damd 965 Champ ad Feema 990 ad Hahe ah geea upple e u f lau he f ped ad ee he ed ped. Ul deed fm ump h ped ad hee eque me. The ume f geea eah ped malzed. Cump he ug deed. The ug ae ue a lump-um a T. The afe-a wage me a ued f ump he ame ped allaed hee ae apal + deed geme d + ad mal geme d + de fae ump ld age +. I add he ug puhae all he mal me M fm he ue ld de fae pa f he ump eeme. Se hee ae eque he ld ume all he ae me. I add he eee lump-um mea afe TR efe he ell he me hldg he ug. 0 The mal me ped gw a ae θ. Thee ae w ue f aggegae he em: a pdu h ad me uppl h. ah ped la N ea al. Capal ued a pu pdu e ped afe whh me pdue alue ze.e. hee full depea. Capal eld a eu +. Bd ae he fm f lg-em geme de wh mau N ea. Ideed d pa a le eal eu ad mal d a le mal eu R. Thee eu ae edgeul deemed ha he mae f deed ad mal d lea. Beaue fla a e fea wh ea mal d pa a eal eu + = R /П + whee П + P + /P he ae f fla. The eal eu me alae hu m+ = / П +. A pe demad f me maed a ah--adae a ld age ump. Fllwg Hah ad Slw 995 he ld ae equed puhae a fa δ f ump ug me alae. Hee M + δp + + whee M + = M + TR + he p-afe leel f me hldg f he ld. Th d f ah--adae a ha ee ued eeal ee pape whh ue elappg geea mdel wh pefe fegh adde ue f pmal mea pl ee e.g. Mhel ad Wglle 005; Gaha 007. A hee pape he ah--adae a aumed d. I eal em he dg ah--adae a mple ha m whee m m m TReal TR eal TR / P ad m M / P. The udge a f he ug ped ae w T m m TR m eal 9 I Champ ad Feema 990 ume hld me apal ad mal geme de u he fla pemum ze. Hahe 04 de a elappg geea mdel wh mal ad deed de ad a fla pemum u me dued a ah--adae a h mdel. 0 Th aump eue ha he ee me paed fm he ue ld he ue ug. Thee eu ae daed a me eaue he lea he mae f d a he dae whe d ae puhaed.e. a ed f ped. 4

5 5 Cume hae CRRA pefeee. The ug f ped le he fllwg plem: ma U.. 4 whee β he du fa ad γ he effe f elae ae. The f-de d ae a fllw: / f apal 5 / f mal d 6 / f deed d 7 whee / ad θ + he me gwh ae ge Se... Ne ha hee ule equa ae -adad due he lu f he em mulpled he effe δ he fa f ld-age ump ha mu e puhaed ug me. Seg δ = 0 ge adad ule equa f he fm =. f = { }.. Fm The pdu e f a epeeae fm ha pdue upu mg apal ad lau a C-Dugla pdu fu. The hae f apal upu equal α ad he lau hae α. The fm he apal ad lau mpee mae a mame ue pf. Tal fa pdu ped deed A. The eal wage ad he eu apal ae ge : A w 8 / A 9 Pdu fllw a AR pe lg: A e A A l l 0 whee e a IID-mal a wh mea ze ad adad dea σ A.. Geme The geme du fal pl ae ad afe e he al uppl f geme de = + ad mm a me uppl ule. Bh deed ad mal de ae -egae uppl 0. Beaue he aalal eul ha fllw ae A full dea f hee f-de d pded Apped A.

6 geeal d uppl ule pefed a h age. Hwee huld e ed ha he aalal eul el he aump ha he d uppl equa uh ha he mdel ha a uque ead-ae aud whh he mdel a e appmaed... Fal pl Real geme pedg aumed f mpl e a a fa 0 < ϕ g < f GDP ha g = ϕ g. Ge d pe he uppl f geme de ad he pah f geme pedg lump-um ae T ae adued eue ha he geme udge a hld ee ped. The lump-um afe ld geea faed pg me de ee he geme udge a. I eal em he geme udge a ge g T.. Mea pl ad lg u fla I de mdel lg u fla aumed ha geme fllw a me uppl ule ha mple ae-leel df a a eal hz mla Hahe 04. I paula he mal me uppl a he ed f ea ge M M N ep M N ep z z N whee Φ > 0 ad ε a IID-mal me uppl a wh mea ze ad adad dea σ M ha h he em ea. 4 Se eah ped he mdel la N ea ad he me uppl he ed-f-ea qua mple ha he mal me uppl a ped ge M N N M ep M whee he me uppl a hae ee deed =..N dae he ea f ped whh he u. Ne ha qua mple ha M /M - = Π / -. Hee qua fla ped ge M / M / / N N / ep 4 qua 4 hw ha pe me uppl a ae fla wheea pe pdu a lwe fla eaue he ae he magal pdu f apal ad hee puh up eeme ump. I al lea fm h equa ha he me uppl a ue f lg u fla. The ed equal qua fllw fm epeaed uu f he pa me uppl N me. 4 I aumed f aalal eee ha me uppl a ae IID. If me uppl a ae pel elaed he he fla pemum lage. 6

7 7.4 Mae-leag ad equlum Se apal depeae full e ped eme ped = +. Def f equlum: 5 A e d d d TR T w R g m m f alla ad pe wh he fllwg ppee f all : Alla d d O Y le he mamza plem f he geea a me ad fa f pdu ae pad he magal pdu; The gd me ad d mae lea: O Y g d m m d d The geme udge a afed ad pedg a a fa f GDP: T g g g 4 The ah--adae a dg: d m The fla pemum: aalal eul Tag a ed-de appma f qua 6 ad 7 ge he fllwg elahp ewee mal ad eal ee ae: 6 a /.. f d R 5 whee ha dee lg dea fm he deem ead-ae ad. The fla pemum he fal em qua 5.e. he aae ewee he ha du fa ad fla. I ell u ha f fla hgh whe he magal ul f eeme ump hgh he mal de wll pa a hghe equlum mal ee ae ume mpeae f he fa ha he eal paff wll ed 5 Ne ha d ad upep hae ee dued h e dee demad ad uppl alue. 6 See Apped B f a dea. Ieegl qua 5 hw ha he elahp ewee eal ad mal ee ae -adad: hee a addal aae em lg ump ad fla ad he effe he fla e em lge -/. The uual epe eeed whe δ = 0. Mahemaall he adad epe : a /. f d R.

8 8 e lw a me whe ea ump hghl alued. Se h aae em dal ped- fma l he mpe f magal ul ha elaed wh uapaed fla ha mae f he fla pemum. 7 The am dee a ed-de auae led-fm lu f he fla pemum. A ed Deeeu ad Suhelad 0 h eque f-de auae epe f he ha du fa ad fla. Lg-leazg he ha du fa ad qua 4 we hae:.. df ad N. Ieg hee eul he fla pemum em qua 5 ge a... N N IRP 6 We heefe eque a epe f ld age ump. Fl e ha he me afe ad he ah--adae a qua allw u we qua a: m 7 whee / he hae f al geme de ha deed. Lg-leazg he la equal qua 7 ad ug he deem ead-ae a he appma p f all aale eep he dea hae ad g ha + = R /П + ad = a he deem ead-ae: 8 R A R A 8 whee θ / θ δ θ ad 0 he appma p aud whh he dea hae lg-leaed. 7 Cequel ρ A ad he apaed pa f fla wll mae f he fla pemum. Ne ha he fla pemum he l geue pemum qua 5 eaue he he aae em -ze ee f huehld ae -eual.e. whe γ = 0. 8 The dea hae appmaed aud he deem ead-ae eaue he lae de deped. Ne ha eaue he me-ag mpe f he dea hae de affe he fde ehau f ld-age ump ee q8 a a pfl hae = wll upp a equlum. Th a geeal eul f ed-de lu ealhed Deeeu ad Suhelad 0.

9 Nw uug f fla qua 8 ad lleg em we hae a epe f ld-age ump em f egeu ad pedeemed aale: N A R O whee A A A ea qua 0. 9 Fall uug qua 9 qua 6 ad g ha me a ae uelaed ge u a ed-de-auae epe f he fla pemum: IRP γ a. N A N M Se eah ped he mdel la N ea he aualed fla pemum a e alulaed ddg he ae equa N. 9 I huld e ed ha he paamee N ee qua 0 del eaue ae-leel df he me uppl a ue f lg u fla a lea fm qua 4. qua 0 hw ha he fla pemum eae wh he effe f elae ae pdu ad me uppl lal. I add deped he ead-ae hae f eeme ump ha fuded mal d θ ; he dea hae ; 0 ad he ead-ae hae f apal me eeme ump θ = θ δ. Pdu ad me uppl lal ee he fla pemum eaue h pdu ad me uppl a wll ed lwe eeme ump ad hee ae magal ul a me whe fla uepeedl hgh. A pe me uppl a ae fla hugh w hael. F hee a de effe fla hugh a e me uppl gwh plu a de effe due he fa ha a pe me uppl a lwe eeme ump ee qua 9 whh u ae fla fuhe qua 4. Beaue uapaed fla edue he eal alue f mal de lwe eeme ump ad ae magal ul. A a eul mea lal ae he fla pemum. Nw de he mpa f pdu a. If hee a uepeedl lw a pdu he he magal pdu f apal wll fall puhg dw eeme ump. A he ame me fla wll e qua 4. Se pdu a wll ed ae magal ul a me whe fla hgh pdu al mae a pe u he fla pemum Fmall d N fllw fm he aump ha aual eld = N-ea eld /N. Th e mm elappg geea mdel ee e.g. Cade ad Meha 00 p Hahe 04 ha hw umeall ha he fla pemum a elappg geea mdel deped he dea hae. 9

10 I lea fm qua 0 ha he fla pemum deped uall he eadae hae f eeme ump fuded mal d θ ad apal θ = θ δ. The d hae θ ha a amguu mpa he fla pemum eaue ag he pfl hae f d mae he ld me uleale uepeedl hgh me uppl a ha lwe he eal alue f mal geme de u al mple a mulaeu fall he pfl hae f apal whh edue epue pdu a. I al lea fm qua 0 ha he ah--adae paamee δ mae f he fla pemum. Th p deed Se The fla pemum: umeal eul fm a alaed mdel I h e a umeal eample deed. I paula he mdel alaed ad he fla pemum mpaed wh eg heeal ad empal ude. The eul eped h e ae aed a ed-de appma f he mdel aud he lg ead-ae a mpued ug Dae ee Adema e al Bd uppl ule T emphae he geeal f he aalal eul Se he dam f geme de hae hu fa ee lef upefed. Th wa ple eaue qua 0 hw ha a ed-de appma he fla pemum affeed he ead-ae hae f d me eeme ump θ u he dam f he d uppl. Se he am h e mpue a meagful mdel emae f he fla pemum a d uppl ule he ha mple a plaule eadae hae f d me eeme ump ad plaule a f e aale. I paula he d uppl ule fllw ha Hahe 04: Th ule mple pefe ump mhg a he deem ead-ae. The deem ead-ae f he mdel ude h ule eped Apped C. 4. Cala The mdel ughl alaed he US em. I paula he paamee f he mdel ae he ughl mah e a he daa. pe f hee e a a he deem ead-ae ae eped Apped C. Se hee a deped up eeal dffee paamee he ala ue paamee alue whh ae plaule ad ge gd pefmae aga age a. The ala led Tale. The eul eped Dae h e mah he ped f qua 0 eal. I me mdel e a ae ped dw a gle paamee ha alaed alue a e e eplae age a eal. The mdel hee de hae h ppe. 0

11 Tale Baele alaed alue α Capal hae 0. θ g Geme pedg-gdp a 0.6 β Pae du fa / Φ Aual ead-ae me gwh.0 γ R ae 5 ρ A Pdu peee 0.50 N Nume f ea pe ped 0 σ A SdTFP δ Cah--adae paamee 0.05 σ Sd me. 0.0 Shae f deed de 0.0 The ume f ea pe ped N e equal 0 mplg ha he d hae a mau f 0 ea. Sead-ae aual me gwh Φ e a.0 e wh ead-ae fla f %. The paamee θ g e a 0.6 mah a geme pedg-gdp hae f 6%. The pdu fu paamee α e a 0. mplg ha apal me % f GDP. Th alue he lw de f adad ala u h help he mdel mah he age a f lg-em de ad eme GDP ee Tale ad Apped C. The ah--adae paamee δ e a 0.05 whh mple ha 5% f eeme ump fuded me. Th ala mple ha ah hldg ae % f GDP whh fal mla he ue mpe f M US daa. 4 Se eal eu ae equaled he aee f uea he hae f deed de de affe he deem ead-ae ee Apped C. I heefe e a 0. mah he 008 hae f uadg maeale de Teau Ifla-Peed Seue ee Campell e al The du fa β e a / whh mple a aual du fa f ad a ead-ae eal ee ae f aud.5% pe aum. Se fla % pe ea he ead-ae he mal ae.5% pe aum. The effe f elae ae γ e a 5. Th alue he hgh de f adad ala ge he mdel a hae f mahg empal emae f he fla pemum. The pdu a adad dea σ A e a 0.07 ad pdu peee ρ A a 0.5. Bh f hee alaed alue ae mla he Hahe 04 wh de a mdel wh a geeaal hz f 0 ea. 6 Fall he adad dea f me uppl a e a 0.0 whh le lghl elw he adad dea f aual M gwh fm aed FRD daa. 4. Reul ad du The alaed mdel de fal well aga age a ee Tale. The US eme- GDP a ha ee le 5% e he ped 99 0 ad e he ame ped he ump hae aeaged 69% ee Tale 0 m Rep f he Pede mplg age a f 0.5 ad The mdel ge a f 0.4 ad The US geme de GDP hae aeaged aud 70 pe e e he ame ped ad aed The aeage geme pedg hae e he ped 99 0 wa appmael 6%. See m Rep f he Pede 0 Tale. 4 See he daa aalale fm he FRD daaae u he Fedeal Reee Ba f S Lu. 5 Ne ha he dea hae a e eaed a a alaed paamee eaue he eu R ad ae edgeu ad we ealhed ee qua 8 ad Fe 8 ha geeal a a dea hae upp a equlum up a ed-de appma f he mdel. 6 The hghe alue f σ A hee he efle he lge geeaal hz f 0 ea.

12 OCD daa d wh maue eeedg 0 ea u le ha equal 0 ea aued f e-eh f all d uadg Mulplg hee w fgue gehe mple a age hae f lg-em de GDP f 7%. O h e he mdel ge a a f Fall he mdel mple ha me fm mal d au f 9% f eeme ump a he deem ead-ae. Th fgue fal mla he e mal p f US huehld aged ad e 75 a a fa f aeage e wh: 9.4% ad 0.4% epeel 989 ee Depe ad Shede 006. The fla pemum he alaed mdel -al a 0 a p pe aum. I fa h fgue mpaale me ee empal emae fm emaed aage affe mdel f he em uue. F ae ela he u Aea Gaa ad Wee 00 emae a fla pemum a a 5-ea mau f aud 5 a p whle Hödahl ad Ta 0 ep a aeage pemum a he 0- ea mau f u e 0 a p. M empal emae fm affe mdel f he em uue ed e mewha hghe ha hee fgue hwee. Tale Ifla pemum ad age eu mdel a Tage Def Deem Sha / 0.07 Lg-em d/gdp / 0.4 Ieme/GDP / 0.69 Cump/GDP Nmal d me Reeme ump IRP Ifla pemum p.a Ne: he alue f g/ ge + / /. The IRP a p pe aum. I he US eeal ee ude hae emaed -aage affe mdel f he em uue ug mal eld ad fla daa alg wh addal fma fm de-led eld fla ue fla wap. Thee ude p a pe aeage fla pemum f ewee 50 ad 0 a p. F ae D Am e al. 009 fud a fla pemum 0-ea d f 64 a p aeage whle Ag e al. 008 ep a hghe aeage pemum f aud 0 a p a a 0-ea mau. e hghe emae a a 0-ea mau hae ee eped Che ad Muelle 0. mae f fla -pema lg-em US d hae ee pded Hauh e al The eul ugge ha fla pema eae wh mau: 0-ea d hae a pemum f 5 a p mpaed 8 a p 0-ea d ad 0 a p 0-ea d. T he auh wledge h he l ud emag lg-em fla pema. Whle h ud lude ha lg-em fla pema ae mewha hghe ha he alaed mdel he mdel ped f he ame de f magude. 7 The daa he geme de-gdp hae wa aed fm he FRD daaae.

13 Thee ae fewe empal emae f fla pema f he UK u hee hae ee me ale ee aemp. Je e al. 00 emaed a -aage affe mdel f he em uue ad luded ha he fla pemum 5-ea d ha aeaged aud 00 a p. Me eel Adeae 0 emaed a New Keea mdel f he UK em ad fud a aeage fla pemum f aud 50 a p 5-ea d ad 70 a p 0-ea d. The eul Rehee 004 lewe ugge ha he UK fla pemum -al a hee ad lge maue. Tug he heeal leaue geeal equlum mdel hae had a dfful me eplag he magude f fla pema u a wh he ae pema. 8 F ae Raea ad Seppälä 007 mulaed a New Keea mdel f he em uue ad fud ha fla pema wee ul mall ad egae a d maue up fe ea. De Pal e al. 00 hwed ha he g f he fla pemum deped uall h mp: pe a New Keea wld dmaed pdu h u egae whe mea pl h ae dma. The pe fla pemum he mdel amu 9 a p a -quae d. I a mla New Keea mdel Hödahl e al. 008 fd e mall pe fla pema f le ha a p a maue fm 0 ea. Lal a ed ae Adeae 0 emaed a New Keea mdel f he em uue UK daa ad fud a aeage fla pemum 5-ea d f aud 50 a p. Hwee h fgue ele uall hgh emaed ae hugh pe- Z pefeee. Cequel he mdel wuld hae ee ale geeae hgh pema f plaule leel f ae had ee mped he mdel ema e.g. plag ud he emaed pefeee paamee elaed ae. I umma he empal leaue p ul pe fla pema ma deelped eme wh lage pema he US ad he UK. Thee ae few ude egag lg-em pema u he aalale edee p a fla pemum f aud 80 a p 0-ea d ad 00 a p 0-ea d. Alhugh he pemum f 0 a p he alaed mdel mewha lwe ha hee fgue f he ame de f magude a m empal emae he leaue. 5 Rue The aal f he peu e hw ha he fla pemum -al a alaed mdel. Th e due he le f he ah--adae a h eul ad egae he e f he pemum e alaed paamee. 5. Impae f he ah--adae a Thee ae w wa ae he mpae f he ah--adae a f he fla pemum. F hagg he ah--adae paamee δ hage he fa f ld-age ump ha mu e puhaed ug me ad ale he mp f eeme pfl. Sed we a a hw he fla pemum fm he alaed mdel mpae wh ha a mdel wh ah--adae me. 8 The dffule ha heeal mdel fae mahg -pema ae well-w ad appl h d e.g. Bau e al. 989; Rudeuh ad Swa 008 ad equ e.g. Meha ad Pe 985.

14 5.. Cah--adae paamee A lea fm qua 0 he ah--adae paamee δ ee he fla pemum del wh h de effe eg amguu. I wll al ee h epe del hugh he effe θ = / he ead-ae hae f d me eeme ump. I he ae f he alaed mdel a e hw ug he epe Apped C ha a e δ wll ed edue θ ude adad paamee alue. Se δ ha a amguu mpa he fla pemum we e umeal aal mulag he fla pemum ude aleae alue f δ. Fg Se f he fla pemum he ah--adae paamee δ. Ne: The fla pemum a p pe aum. The aele ae δ = Fgue hw ha he fla pemum elael ee δ. F ae dulg he alue f δ fm he aele alue f lwe he fla pemum 8 a p wheea edug 0.0 ae he fla pemum a p. Alhugh Fgue eem ugge ha eg δ = 0 wuld ae he fla pemum h ae eaue me ad hee fla ae. Ug uh a ehma leal ele eaue mple ze fla pemum def. Iead me apppae mpae aga a ae whee me alued u he ah--adae me ae. We w u a mpa f h d. 5.. Aee f he ah--adae me Champ ad Feema 990 de a elappg geea mdel whh me dued a legal equeme hld eal me alae f a lea μ > 0 ha m = μ f all whe he a dg. A a eul me ha alue equlum u he ah--adae me ae. T ae he mpla f h a aalal epe he fla pemum wa deed ude h aleae aump ee Supplemea Apped. The fla pemum w ge IRP N M whee a peul θ / he ead-ae hae f d me. If h aleae mdel alaed wh he ame alue f N ad σ M a he aele mdel ad he pdu fu paamee α he ge he ame d hae θ he he peded fla pemum muh lwe a l 5.4 a p pe aum. Th fdg hw ha he ah--adae me ual pdug a zeale pemum. I paula ae he fla pemum alm 5 a p pe 4

15 aum ad me ha ele alue. I al ale ha pdu de mae f he fla pemum he aee f he ah--adae me. The ah--adae a mpa f he fla pemum f w ea. F mple ha fla pel elaed me uppl gwh u eel elaed eeme ump; ee qua 4. Cequel he pe ela ewee ha du fa ad fla ge ha he aee f he ah-adae me. Sed eaue fla deped mea gwh ad eeme ump fla deped h pdu ad mea lal. B a all fla me fm mea lal he aee f a ah--adae me ee he Supplemea Apped. A a eul fla hghe f a ge leel f lal he ah--adae mdel. 5. Paamee e aal Th e de ue eeal e alaed paamee amel he effe f elae ae γ he dea hae mea σ M ad pdu σ A. A hw Apped C hee paamee d affe he mdel deem ead-ae. Cequel he a e aed e ue whle maag he deem ead-ae led Tale. The eul ae hw Fgue. Fg Se f he fla pemum e paamee. Ne: he fla pemum a p pe aum. Wh he eep f pdu he fla pemum que ee hee paamee. Ude hgh ae f 7 he fla pemum e alm 0 a p whle ude a adad paameeza uh a fall aud a p. Ce wh qua 0 he fla pemum fall a a lea ae a he dea hae eaed. I fall fm 4 7 a p a he dea hae eaed fm whh appea e he m elea age f ma deelped eme. 9 F mea lal hee al deale e: ag he 9 F ae Caada 008 deed d wee aud 6% f maeale geme de Depame f Fae Caada 008. Smlal Campell e al. 009 ep ha 008 deed geme d wee 0% f maeale geme de he US. I he UK whh ha he hghe dea hae amg deelped eme he dea hae ha ee ewee 0% ad 0% e he pa deade. 5

16 mea a adad dea 0.05 ae he fla pemum alm 0 a p whle lweg 0.05 ge a fla pemum f aud 5 a p. B a ag he adad dea f pdu a fm ae he fla pemum l mdel fm 7.5 a p. All all he lu ha he mdel pdue a -al fla pemum fal u wh he fla pemum fallg elw a p. 6 Clu Th pape ha egaed he fla pemum lg-em geme de a elappg geea mdel. I de apue lg u fla me uppl h h he em a a eal hz ad lead ae-leel df. The pape mae w ma u. F ug he mehd deelped Lmad ad Suhelad 007 ad Deeeu ad Suhelad 0 a ed-de auae led-fm aalal epe f he fla pemum wa deed. Th epe hw ha he pemum deped uall he mpae f mal d ad apal a ue f eeme ump. Th fdg appealg eaue he daa ugge ha a mpa ea ld huehld ae h uapaed fla he uaal hldg f mal geme de Depe ad Shede 006; Meh ad Teama 0. The ed u wa hw ha he fla pemum peded he mdel -al ude plaule ala f ae. I paula whe he mdel wa ughl alaed US daa gae a fla pemum f aud 0 a p. Th ume f he ame de f magude a m empal emae ad fal u e aal. I he mdel peeed me wa dued a ah--adae a ld-age ump. Th aump ual eaue ae fla ad eghe he ela ewee fla ad he ha du fa. I fa he fla pemum lweed l 5 a p he ame mdel f he ah-adae me ae. Awledgeme: The auh wuld le ha Chale Nla ad Jame Malle f helpful mme. Th eeah wa fuded pdal fellwhp PTA fm he m ad Sal Reeah Cul UK. 6

17 7 Apped A Dea f f-de d Th Apped dee he f-de d f huehld eped he ma e. T a wh e ha he udge a qua ad a e we a fllw whee he lump-um mea afe he ld ae a ge he ld: m T w A eal m TR m A whee ad wh hae / / ad. Reaagg f + A ad uug he eul A ge u he lfeme udge a faed he ug ped : eal m TR w A whee he fa ha / m ha ee ued. Due he ah--adae a m + = δ + he la em A wll e a fu f ump ld age. I paula ge ha Π + P + / P ad M + = θ + M : m P M m A4 Suug f A4 A ad lleg em ge eal TR w A5 The mamza plem f he ug ped a heefe e aed a fllw: ma U O A6. eal TR w

18 The f-de d f h plem a fllw: / A7 whee /. The ule equa f ddual ae hldg ee Se. a e aed fm A7 eg f { } he def f +. Apped B The elahp ewee eal ad mal ee ae I h Apped he ed-de auae appma mehd Lmad ad Suhelad 007 ued dee he elahp ewee eal ad mal ae. Th mehd appled pfl plem Deeeu ad Suhelad 0 amg he. F eee he f-de d f d hldg ae epeaed hee: ~ f mal d B ~ f deed d B whee / ~ /. ~ R ad - / / We a ag a ed-de appma f B ad B: ~ / / ~ ~ O B ~ / / ~ ~ O B4 0 0 whee ha dee lg dea fm he deem ead-ae ad O lude all em f hghe de ha. Suag B4 fm B ad gg hghe-de em we ge: ~ ~ ~ / ~ ~ ~ B5 0 A ed Hödahl e al. 008 ad Deeeu ad Suhelad 0 ed-de auae epe f ae pe a e aed fm f-de auae lu. I paula em lg pdu a e mpued ug he lg-lea uepa. 0 T h ed e ha he eu ha ee qua B ad B a e appmaed f-de aud he deem ead-ae a fllw: 0 See Pp Deeeu ad Suhelad 0. 8

19 9 ~ B6 ~ B7 Ng ha ad R we a mplf hee equa ~ R B8 ~ B9 whee ad. Due ea equalee he lg-leazed eu B8 ad B9 mu af: ~ ~ B0 Th ea mplfe mewha he dea whh fllw. F ag epea B5 ad ug B0 em ha le pdu ge a ed-de auae epe f he epeed dffeee eal eu lg ed mme l: ~ ~ ~ a ~ a ~ ~ ~ ~ ~ ~ B Ug B8 ad B9 mpue he em he RHS f B we hae: a a ~ a B a a ~ a B a ~ B4 a ~ B5 The ed equal ue a z z z ad z z z alg wh equalza f epeed eal eu a pe B0.

20 Suug hee epe he ed le f B mple ha ~ ~ a B6 Fall B8 ad B9 he lef had de f B6 equal ~ ~ R B7 Suug B7 B6 ad ddg ϕ ge u he equa eped Se : R / a d f B8.. Apped C Deem ead ae f he alaed mdel ad e a Deem ead-ae T m C m m TReal / C TR m C eal m / C4 m m C5 N C6 ~ / C7 ~ ~ ~ C8 R C9 A C0 C C w C / / C4 / / C5 g C6 g T g C7 / g / C8 mplg ha C9 0

21 Deem ead-ae a m C0 / C g g C / g C / / g C4 / g / g C5 Refeee Adema S. Baa H. Jullad M. Kaamé F. Mhu F. Peeda G. Pfefe J. Ra M. ad Vllem S. 0. Dae: Refeee Maual Ve 4. Dae Wg Pape N. CPRMAP. Adeae M.M. 0. A emaed DSG mdel: plag aa mal em pema eal em pema ad fla pema. upea m Reew 56 pp Ag A. Beae G. We M The em uue f eal ae ad fla epea. Jual f Fae 6 pp Bau D.K. Geg A.W. Z S R pemum he em uue. Jual f Mea m 4 pp Beae G. Wag X. 00. Ifla ad he fla pemum. m Pl 5 pp Beae B Wha plmae a lea fm ae pe. Speeh he Ieme Aal Se f Chag Chag Ill Apl 5. Campell J.Y. Shlle R.J. Vea L.M Udeadg fla-deed d mae. Bg Pape m A :009 pp Champ B. Feema S Me upu ad he mal aal de. Amea m Reew 80 pp Che M. Muelle P. 0. The em uue f fla epea. Jual f Faal m 06 pp

22 Cade G.M. Dald J.B. Meha R. 00. Ju a w: a ew pepee he equ pemum puzzle. Quael Jual f m 7 pp D Am S. Km D. We M Tp fm TIPS: he fma e f Teau fla-peed eu pe. Fae ad m Du See Wg Pape 00-9 Fedeal Reee Bad. De Pal B. S A. Weee O. 00. Ae pg mpla f a New Keea mdel. Jual f m Dam ad Cl 4 pp Depame f Fae Caada 008. De Maageme Rep Aalale a: hp:// La aeed: Mah Depame f Fae Caada 0. De Maageme Rep Aalale a: hp:// La aeed: Jul Deeeu M.B. ad Suhelad A.J. 0. Cu pfl pe em mamdel. Jual f he upea m Aa 9 pp Damd P.A Naal de a elaal gwh mdel. Amea m Reew 55 pp Depe M. Shede M Ifla ad he edu f mal wealh. Jual Plal m 46 pp Gaa J.A. Wee T. 00. Ifla ad fla pema. CB Wg Pape 6. Hah F. ad Slw R A al ea mde maem he. Bal Blawell. Ofd. Hahe M. 04. Ideed eu mal geme de ude fla ad pe-leel ageg. Jual f m Dam ad Cl 45Aug pp Hauh J. Peah G. Rhe P mag eal ad mal em uue ug ug Teau eld fla fea ad fla wap ae. Fedeal Reee Ba f Cleelad Wg Pape N Hödahl P. Ta O. 0. Ifla pema he em uue f ee ae. Jual f he upea m Aa 0 pp Hödahl P. Ta O. Ve D The eld ue ad maem dam. m Jual 58 pp Je M.A.S. Lldhld P. See S. 00. ag fla epea ad fla pema fm he em uue: a mdel f he UK mal ad eal eld ue. Jual f Bag ad Fae 4 pp Lmad G. ad Suhelad A.J Cmpug ed-de auae lu f aal epea mdel ug lea lu mehd. Jual f m Dam ad Cl pp

23 Meh C.A. Teama Y. 0. Ifla Nmal Pfl ad Wealh Redu Caada. Caada Jual f m 44 pp Meh C.A. R-Rull V.J. Teama Y. 00. Aggegae ad welfae effe f edu f wealh ude fla ad pe-leel ageg. Jual f Mea m 57 pp Meha R. Pe.C The equ pemum: a puzzle. Jual f Mea m Raea F. ad Seppälä J Mea pl epeed fla ad fla pema. Reeah Du Pape 8/007 Ba f Flad. Rehee A Cdal fudg f fla-deed ad eal geme d. Jual f Bag ad Fae 8 pp Rudeuh G.D. Swa.T amg he d pemum puzzle wh a DSG mdel. Jual f Mea m 55Suppleme pp. 6. Supplemea Apped f le pula l The fla pemum he aee f a ah--adae a I h Apped he fla pemum deed he ae whee fllwg Champ ad Feema 990 ug age ae equed hld eal me alae f a lea μ > 0 ha m μ. A ha pape h a aumed d ha m = μ f all. All he ape f he mdel ae uhaged. Th hage aump affe huehld fde d ad he equa f fla ad ump he ld. The f-de d ae deed ad he mpla f fla ad ump he ld ae dued. Fall we u he fla pemum. F-de d We a g ha he udge a a e we a fllw whee he lump-um mea afe he ld ae a ge: w T m SA m TR SA m eal whee ad wh / / ad. Reaagg f + SA ad uug he eul SA ge u he lfeme udge a f he ug ped : TReal TReal w m w SA whee m / ad m = μ hae ee ued.

24 4 Hee he mamza plem f he ug ped a fllw: ma U O SA4. eal TR w The f-de d f h plem : SA5 The ule equa f ddual ae hldg a e aed fm SA5 eg } { f he def f + : f apal SA6 f mal d SA7 f deed d SA8 Thee ae he adad ule equa he aee f a ah--adae a. qulum fla ad ump he ld The eee equeme m = μ mple ha M /P = μ whee M he mal me ad P he aggegae pe leel. Cequel fla equal he me uppl gwh ae ee qua f he ma e: N N M M M M P P ep / SA9 Tug ump he ld e ha e he mea afe equal eal em m + m+ m ad m = μ we a we qua f he ma e a fllw: m SA0 whee / he hae f geme de ha deed. The fla pemum Se + = R /Π + ag a ed-de appma f SA7 ad SA8 lead

25 5 a f d SA a a R SA The fla pemum he aae em. We a dee a aalal epe f h em a fllw. F deg he fla pemum IRP we hae O IRP SA Sed lg-leazg SA0 ad g ha = a he deem ead-ae: O R A R A SA4 whee / ad / /. Fall uug SA4 SA ad ug SA9 we fd ha 0 a M N R A IRP SA5 Th epe mahe he e eped qua f he ma e. A he ma e he dea hae appmaed aud = whee 0 ; ee qua 8 ad Fe 8. The eulg dea hae a a = a pe he du he ma e.