Part 2 Models with Money

Transcription

1 a 2 odel wh oney Ba efeene: Blanhad /Fhe hae 4/5 Gal o Woodfod hae 2 2. hallenge A oly h wll e addeed n a 2 of he oe: How doe oneay oly affe nonal e / eal eonoy? Wha he adeqae degn of oneay oly? Wha he ak of enal ank? How o oe wh nenve ole? How hold we defne e aly? I hee a ole fo ave alaon oly? How an oly e leened n he eene of neany? an oney o nee ae ageng leen oal oly? Ba: oden New Neolaal Synhe - Key feae: AS ve geneaed y ky nonal e. 2 AD ve deved fo neeoal oaon le eqaon 3 L ve ovaed y enal ank oly oney ly o nee ae le. Refeene on: Fonle val eonoy eal ne yle aoah/ oden oha gowh heoy: laal dhooy: n he aene of nonal and eal fon: flele e eonoy wh effen ake ooe B heoy: ofondaon o ovae a ole fo oney How o node a ole fo oney n he neeoal faewok? Key hallenge: a In neolaal eonoe wh olee e of ake: no need fo oney all ona aanged aleady a he a of he eonoy. oney a donaed ae ond and ohe ae ean ove en wheea nonal en of oney fed o zeo Wh nflaon: eal en negave oney nnally ele no de ly o of holdng /onng oney al: elf flfllng nae of oney: I hold oney only f I an ha lae ohe agen wll ae. oney a oal onvenon! adng fon ae al: hee ha o e a need fo lqdy. any oeng one Sdak odel: A ho nlde oney n ly fnon. ah-nadvane odel and he hong e odel an e een a ovang eal ae of he IU aoah. F we a wh an old fahoned aoah j ang hee a deand fo oney! We ak: how wll he e ah e deened? 65

2 2.2 oney and Inflaon agan odel of oney and e Fhe eqaon: π Logah aoaon: π agan oela oney deand fnon allow lnea analy: o: d wh d d ln Deenaon of he e Level fo a gven oha oney ly ah { } 0 }: ql on he oney ake: gve lnea dffeene eqaon: d Fowad lookng olon: e level a fowad lookng vaale non edeened Se 2. Ue law of eaed eeaon 2 2 o ge

3 Ieaed on gve: 0 l 0 Ae ha he onvege < l 0 Rle o hyenflaonay le: Ioe eon 0 l Solon: 0 F So he e level deened y fe fndaenal Sefy eeed fe oney ly oe! ale: A onan oney ly: 0 B onan gowh ae of oney: 0 0 Noe:

4 Anaed neae n oney ly a oe fe dae : > < D Soha oney ly wh AR oe: ε ρ 0 ρ 0 ε So ρ So 0 0 ρ ρ ρ ρ D follow a ando walk ρ : D2 eally noelaed: 0 ρ : ε Oen e: A Raonal of oney ly oe B Raonal of lng o hyenflaonay le Raonal of oney deand ofondaon fo L ve 68

5 A Raonal of oneay oly: eae egnoage Hyenflaon a oneqene of he need o fnane govenen endng Segnoage fo oney eaon: S Seady ae govenen evene fo oney eaon? Wh onan oney gowh ae Segnoage : S agan: Ioela oney deand onan oe of oney gowh: geneae: o: S. a egnoage a: S 0: fo 2 0 S π onno e analy: Oal ly fo onool who o B Ble e S π e Fowad lookng olon gve f ode dffeene eqaon: π 69

6 One olon of h dffeene eqaon : F 0 Who addonal anho ha eqaon dffeene ha any ohe olon: F F y y no efed who oe endon onan Ae he followng oha oe {y }: 2 y y v wh 0 v o y y F y alo a olon o he dffeene eqaon. Wh l y l y y y a le wh y elodng a he ae /. Solon o he dffeene eqaon onan een vale. nqe olon only f he no-le ondon F hold: l 0 ono ovaon? Unlke No onz Gae ondon: Self flfllng nflaonay eeaon elave hyenflaon ay ake oney ele a a ed of ehange who volang aggegae eoe onan! oney ha o e eenal o le o h a e ah! oeono fondaon fo he oney deand fnon! 2 oe geneally: a oha ng le an alo e a olon f: y v y v wh o wh 0 wh o v 70

7 2.3 oney n he Uly: Bok/Sdak odel enon of andad gowh odel o nlde oney: ee: Blanhad /Fhe hae 4/5 Woodfod hae 2 Walh hae 2 ognal ae: Sdak 967 Bok 974 oney one of any ae oe fnanal oe eal. I nnally ele ovde no de ly. I nonal en donaed y en on afe ond. B oney yeld anaon enef aed y efeene: e eod ayoff fnon: U aed o e onave and neang n oh agen 0 / 0 U > 0 U / 0 Wh /. Sho o odel lqdy eve nde ly deved fo anaon o hong e odel ah n advane onan OLG Feqenly aed: Addve eaaly: V 2 hee oe on of aaon fo eal oney alane: Saaon level wh U 0 and U < 0 fo > Reeenave Hoehold ae: 0 U je o Ineeoal Bdge onan 2 ndon onan No-onz gae onan Folae he elevan dge onan wh a olee e of nonal ae efe foegh e endowen eonoy Inal wealh W gven ndowen ea of nonal ne noe Y - gven 7

8 hooe / and he alloaon of nonal and eal ae B K fo a gven eqene of neeoal e { } and {Q }. Nonal don fao defne: Q Q ν Qν ν ν ν he kle ho e nonal nee ae : Q Ineeoal Bdge onan hee ae dffeen ng onvenon n dee e analy. We e hee he noaon of Woodfod In an alenave ng onvenon fnanal ake oen a he egnnng of eod and agen have o hooe B and K. hen agen eeve noe Y and an one fo lqd ae. hen oney alane a he end of eod ae Y - -. So hee oney ovdng lqdy no he oney held a he end of he eod. How doe h alenave onvenon affe he el? ee Woodfod Aend A 6. 72

9 Defne he egnnng of eod wealh a W B - K - : nonal en fo kle one yea ond B held eween and e. en fo eal ond K Relevan ae vaale: oal wealh W gven a. lnae B o folae he e eod dge onan a he evolon of nonal wealh: W W K Y How o deve h eqaon dyna oaon wh any ae? Ae f ha all ae ae nveed n k-le ond o aal none n oney. Rk-le ond ay nee o Q /. Boh ond and aal ogh la eod deene een wealh y W - B - - K -. Byng oday ond B and aal K yeld wealh ooow W B K. So dge onan an e folaed a: B K Y - W o In e of wealh elnang B a W / K - / Y - W If a of ae ae held a oney wh nee : B K Y - W wh ne eod wealh: W B K! lnang agan B gve wh wealh W a ae vaale. 73

10 2 ndon onan 2a W 0 gven. 2 W 0 Solveny onan: a he enal dae ae lef anno e negave. O no onz Gae onan Q0 W 0 Fo l Q W 0 le: Q y W en de anno eeed een vale of fe ne noe. Solve he oaon ole ng he andad Lagangan aoah: 0 U λ[ Y W Q W 0 λ0 W0 - λ Q W K h gve a FO: a λ λ Q λ Aage eqaon / Fhe eqaon ohewe: ehe B 0 o K 0 [ B 0 K 0! d / λ oney deand L ve 0 e anvealy ondon: λ Q W Q W 0 o l Q0 W 0 74

11 Q ' ' a gve: o ng : ρ ρ 2 / oney deand ve neeaon of FO ondon: RS eween onon oday and ooow eqal o I eal don fao d d ρ 2 RS eween onon oday and onon of eal oney alane eqal o oony o of holdng oney alane een vale of nee lo ne eod de o holdng oney: d d / / oaed veon of he L ve Fo FO fo oal eal alane we an deve a oney deand fnon whh n geneal alo deend on he onon level [eae of ' U 75

12 2.3 Aend: Fhe eqaon nde neany When nflaon oha we need o odfy he Fhe eqaon. le eqaon fo nonal ond: Q ξ ξ Q ξ ξ o q ξ ξ Defne hen fo holdng nonal ond fo all ae of he wold ξ : FO: Q q o eeed en of nonal ond: Q q le eqaon fo eal ond Real e of eal ond: Q q ξ ξ Doe he Fhe eqaon hold nde neany? We aged: q q Q π? Ovoly h only an aoaon degadng ovaane! Ae ha q jonly lognoal ded Fo eng noal we have: [ [ e [e 2 Va So fo and y eng lognoal we ge: [ln [ln e [ 2 Va ln [ln e [ [ [ y ov y y 76

13 ln l n ln π ln q ln q e ovln q ln ln q ln ovln q π ln q ln e [ln Va[ln ovln q 2 π ln π Va[ π ovln q π 2 ln q ln - So: Va[ π ovln q π 2 π So we need o ake no aon an nflaon k e: Va ovln π 2 [ π q B we ally degad nflaon k e aoang he Fhe eqaon: π 77

14 2.4 odel fon ovang nde ly of oney: ah n advane and hong e odel 2.4. ah n advane onan ee anaon ehnology: Soe good - ah good - an e ogh only y ayng n ah:. onon of ah good aed y onan a eal ae of he IU aoah. Reeenave hoehold ha no de ly fo oney holdng. She ae: a U.. 0 ρ Flow dge onan: X W K Y W 2 ah n advane onan fo ah-good X fo all Lagangan lle fo oh onan: λ and ν 78

15 0 l U a [ 0 X ν [ W K [ 0 X W Y FO: w U 2 w U ν 3 w ν 4 w W 5 w K 0 [ o 5 Fhe eqaon 2 U U ν 4 X X ρ ρ 2 4 X X X X ν ν Fo onan > ndng gvng a ove deand fo oney. Se / n he ojeve fnon: ozaon ole foally eqvalen o a nde ly of eal oney and ed good. 79

16 2.4.2 Shong e odel anaon ehnology: eal eoe ed when oned wh eal oney alane avalale. oney ede anaon o hong e eqed fo hang good. wh > 0 < 0 anfo o a o aze nde ly fnon V U f. onde onno e ole: a V 0 [ n e 0 ρ d odfed dge onan nldng anaon o: W n o: 0 0 e d [ π e d B0 0 0 [ w n e d 0 0 Redefne go onon a:. neang n nve fnon o f. anfo no nde ly fnon: ρ a V 0 [ f n e d e d 0 [ π e B [ w n e d d Foally eqvalen o IU aoah. Fo eogeno ly n y V U U f wh efed y:. lao 80

17 2.5 Deenaon of he e Level Analye he followng qeon: a Wha deene nal e level: o ney ly? Inode govenen dge onan Analye ondon fo eneal y of oney gowh odel d ondon fo nflaonay le agan odel e Soha eonoy: Analye dyna eaon o hok f Inode e gde eqe e eng Real effe of oney ae led a long a e ae flele. Hee: look a deenaon of nal e level and le Ble and elf flfllng nflaonay eeaon Ioe addve eaale ly: V and noalze onde oela ly fnon: σ α α U U [ / σ FO gve a L ve: α α oe geneally fo he S ly fnon: U α FO gve a L ve: α α α 8

18 Deenay of he e level Deene he e level fo a gven oney ly oe. Dyna elaon eae eal oney alane deend on he eeed e ah: a eaon ao fe oneay oly ha a on en oney holdng ole: elf flfllng le fo e ah How o ovde a nonal anho? Noe: Fng nonal ae of nee leave e level ndeenae oney ly endogeno FO fo eal oney alane an e efolaed a: Analye a eady ae fo eal eono y: Y wh ρ oly of onan oney gowh onde. Rewe FO a: ql haaeed y he dffeene eqaon: A F G wh F Y Y and G Y W and anvealy ondon l 0 B l G 0 wh G U 82

19 Fo addve eaale ly V we have: F Y V and G Y A eady ae * wh * and V * onan o V * F* G * o Y ρ e fo ρ ρ Fo * wh V 0 f aaon level e ρ Deflaonay e ah: / ρ [zeo nonal nee ae Noe: eady ae * nale eae V '' < 0 o Δ > 0 fo >* Wh fowad lookng ehavo aonal eeaon he n e lev el 0 and e ah 0 e ae nned down nqely f he nale ah an e led o a volang oe onan! 83

20 an we le o dvegen ah? A love eal oney ah deflaonay e ah. * < 0 < <... Real alane ae elodng: 0 anno e an eql f onded fo aove! anvealy onan le o deflaonay e ah. l G l 0 B l aon hee: hee ae no govenen ond See Woodfod hae 2.4 B Hyenflaonay ah Self flfllng hyenflaon: If oney no al he e onoy onvege o a ae eql: l 0 Fo 0 G Y 0 and F Y V 0 V Key: Wha haen o l V? 0 Fo l V ' 0 any ah leadng o l 0 an 0 e an eql Ble led o f l V ' > 0 0 Beae Δ < 0 fo 0 volae law of oon: eal oney gowh anno e ly negave a 0. oney e eenal: agnal ly of oney neae fae han he ae a whh oney goe o zeo. 84

21 Sef ayoff fnon: A S ayoff fnon law of oon: & ρ l V ' l 0 0 / σ / σ > / σ V : / σ 0 fo σ < B Inde ly fo he agan deand fnon: ln ln ln ln V ' >0 fo > ln ln V V '' < 0 l V ' ln 0 0 l n & Fo onan ae of oney gowh: & [ln ln 0 h fo eady ae: 0 e addle on aly Self flfllng elove e ah gh no e led o fo ha ae j he ode ae. Now: look a alenave a dffeen efaon of an nee ae oly. 85

22 2.5.2 oly of a e nee ae eg Sagen/Wallae { } F nonal nee ae: wh 0 oney ly endogeno a All eal vaale ae well efed: Real alane ae nqely deened y: V Rae of nflaon nqely deened Fhe eqaon: π No elave le fo he e ah. B: Inal e level 0 no efed - hee nonal ndeenay: If 0 wh 0 a olon o V 0 hen alo any λ 0 wh λ 0 Dffeene eqaon: [ - onan no ffen o n down he nal e level: If ln a olon whln hen aloln α wh ln α Key Leon: e nee ae eg leave e level ndeenae In ona feedak nee ae le ae ale o onol e level: Inee Rae Feedak Rle ale: Inflaon ageng/ o e Level ageng Annoned edle enal Bank Rle: f π π* Unde wha ondon do we ge a deenae e level? eed nee ae: f π π* Iled dyna of nflaon ng Fhe eqaon π : 86

23 π f π π* F ode dffeene eqaon fo nflaon. Fowad Lookng Solon: π π * π f Analye efe foegh olon ng π * 0: π π* f π π * π π * π S π* S f Unqely deened dyna of nflaon only f f>! In ha ae alway eveal o π* afe devaon fo he nflaon age: π π *! Fo f< nfne ne of olon deendng on eeed nflaon π Fo f> he e level alo nqely deened ng π we ge he eond ode dffeene eqaon π f * * π 87