Lecture 4: The 3 equation model
Date.
=7 Central Bank
- Obiectives of antral bonk
•Whill ditt CBs haut varging mandats, thers prindry gual is fevser
on pria stobility 270 inttedon
Pamorg objectve: to mantan low and stable illetin (ps staboty
-Secundory okijectires:
Full Empliymunt: max sustaineble bul ot enploymurt
7Econemie grouth: supporting sustainabl ond non intlelienang grouth
7Fiapmial Stabilitg: ensure rosihence of tmonciel system
> Erchange rek stability. maintain stable vahe ut curidaу
•CB folus on illatiun os it lacks tool to diceetly inllunes ling con suppply
Equilibuur ate of usmpligmunt Catnhch mllaton is constorl) dilrmml by
supply side stuctrel Haturrs
- Touls of Moitory Policg
•Duernight numinal intrest role: primeng toul
i=rt CB adjust this to intluinG bercuring leste
•Morsy supyly: histoccolly moin lool betore 1980
ag. Hach 0obe
Non conventional policres : used when standord ntrest rale chonges insntficies
7 Quontdatine Gusing CaE): injeed meny direetly into tnunual system by
parchasing assets.
Reserves nad gold -monogiag notund goldand witaey resemes
Role of Catral Bonk (Demoad slabilsing by intuest r06s
CB i intrest rell, dumpers AD. Econamy
gradually retuins to MRE empligmunt
with torget intlaticа
Gwsl
ש
Jigreate to Medium run
Fratlation
Demund side Actual Emyligourtar equal to equilirivon 1B rg
Constantinllatnowe stal CB
use then/ MROJ fallagintlatus
piatlatun
CB I alesl rolk, I AD, ewnomG grapreg
etorns to MRE empliynint with farget
in flaton
, Date.
- Modelling a luntral Bank
CB seeks to miniise a loss fonction (L), whab captuits the lost at
diviations frum fargets:
T
しこり・ツ (CB sety, Сеxоgеn)
• Bliss point the idial state
is whire oulpul is al equilibrivm lye) oud
intletion is ot target (n?)
The bank is equally concirnd about denatioas obove or belon turet
• Intlotion Aversion (B)
4 B=1 : belonud praterenas; indefferene curres are cich
GB71nflation aversei cusues are horizentel ellipsoids. The Co tode
large outpnt losses for smoll intlution gu113
L7 B c1: unimpliyment averse, curves are vectical ellipsrid
- why gout hondove. intlution turget to (b?
• moetory ppolicy is a pretiinedstabilsation toel, politrcally wateal
and more etticital ,as imploenting Piscal Piliry ceguit pariemnt opprew
gout lack low intlotion credibility, os its poldecally motivotd for TAD
LB have higher credibility delidring lou & stoble intlation
The adeption ot inllation target Guds to lowe ond stoble influtien
- CB inditterena curre
다 レンレッーッポ²BCカーオリ²
ㅔㅅ
llath, huizondalellpsunds
万イ
7y yq=yT
y
= Constraints for Policy choics (Bno valionited ferdon to set outpatend
-Genical Ecunomie cunstrant
•Zero Loiner Bound: niminal nuestcate connet fall co ond linit (B abulity
to stimalate ecunomy during diep rearssions a deflatiomory trup
•Fixed exchonge cal: it county toe cvireacy to anathur, cobs foeus on
en eeshorge
thon slabiln
Constaint within the modt:. Plprmeg soply sicde censtrant-objectn eadef
betheen y and a thal 1B must acupt in shode
Polin fargel lyt, 1) assume ут=уea
, Date.
=7 Monetary Rull Curve(MR)
カ
- MR shers the optimal output cinllatin combrotien for any DC CB tou
PCCが²=ろ)
A Pしもれとって) •Slep Finding tongencins
ก2 Por any given PC, the CB lools fur the poird
thwt touchesits smallist possibu loss crde
MR
This represents the min loss achied guen the
supply side constraint
StpJoining tongencios
By cwnructng thest optimal ponts CA,B,C)
across voorlous Pc, we derive MK
Cudjuslm.r pulh)
•The MR curve reprisents the path alory which Cs
will steer the economy back to Bliss Poid
following shock
-2t B is zero, thi MR curd is vertica!
24 B is verg high, the MR cune is flatur
- DerNution ot MR equatin
(= (ge-y?)2 1 BCHC- TJ o st. Ti= 1 t aC ye-gen)
カンTレール
He Hetalyeyea) @
Eay ,nte
しこしgビーサィa」² BCしARしりでDen) 毎が
dL
1= 2lye=yea) +2B [ Te-1 t alye-yz) -7'](x) =0
lge- yeu) = -2df [e -7= # (B7)
lyt-yeq) =-aB Cte - 1) -MR lu
• Negatid sign indiictes that it ratlatica uboe torent b 7tt) thi сB
must cnate a negutice output gop lye cyea) to bring it dion
• a: it PL is stuep Chighd), a smaller ontput gap midect to
achikt specitic redactua inintletua
B: it CB is higklyintletion uvese (hgh B), it will chrosea
larger putput gep to hit the intlaten tengat fastere
Date.
=7 Central Bank
- Obiectives of antral bonk
•Whill ditt CBs haut varging mandats, thers prindry gual is fevser
on pria stobility 270 inttedon
Pamorg objectve: to mantan low and stable illetin (ps staboty
-Secundory okijectires:
Full Empliymunt: max sustaineble bul ot enploymurt
7Econemie grouth: supporting sustainabl ond non intlelienang grouth
7Fiapmial Stabilitg: ensure rosihence of tmonciel system
> Erchange rek stability. maintain stable vahe ut curidaу
•CB folus on illatiun os it lacks tool to diceetly inllunes ling con suppply
Equilibuur ate of usmpligmunt Catnhch mllaton is constorl) dilrmml by
supply side stuctrel Haturrs
- Touls of Moitory Policg
•Duernight numinal intrest role: primeng toul
i=rt CB adjust this to intluinG bercuring leste
•Morsy supyly: histoccolly moin lool betore 1980
ag. Hach 0obe
Non conventional policres : used when standord ntrest rale chonges insntficies
7 Quontdatine Gusing CaE): injeed meny direetly into tnunual system by
parchasing assets.
Reserves nad gold -monogiag notund goldand witaey resemes
Role of Catral Bonk (Demoad slabilsing by intuest r06s
CB i intrest rell, dumpers AD. Econamy
gradually retuins to MRE empligmunt
with torget intlaticа
Gwsl
ש
Jigreate to Medium run
Fratlation
Demund side Actual Emyligourtar equal to equilirivon 1B rg
Constantinllatnowe stal CB
use then/ MROJ fallagintlatus
piatlatun
CB I alesl rolk, I AD, ewnomG grapreg
etorns to MRE empliynint with farget
in flaton
, Date.
- Modelling a luntral Bank
CB seeks to miniise a loss fonction (L), whab captuits the lost at
diviations frum fargets:
T
しこり・ツ (CB sety, Сеxоgеn)
• Bliss point the idial state
is whire oulpul is al equilibrivm lye) oud
intletion is ot target (n?)
The bank is equally concirnd about denatioas obove or belon turet
• Intlotion Aversion (B)
4 B=1 : belonud praterenas; indefferene curres are cich
GB71nflation aversei cusues are horizentel ellipsoids. The Co tode
large outpnt losses for smoll intlution gu113
L7 B c1: unimpliyment averse, curves are vectical ellipsrid
- why gout hondove. intlution turget to (b?
• moetory ppolicy is a pretiinedstabilsation toel, politrcally wateal
and more etticital ,as imploenting Piscal Piliry ceguit pariemnt opprew
gout lack low intlotion credibility, os its poldecally motivotd for TAD
LB have higher credibility delidring lou & stoble intlation
The adeption ot inllation target Guds to lowe ond stoble influtien
- CB inditterena curre
다 レンレッーッポ²BCカーオリ²
ㅔㅅ
llath, huizondalellpsunds
万イ
7y yq=yT
y
= Constraints for Policy choics (Bno valionited ferdon to set outpatend
-Genical Ecunomie cunstrant
•Zero Loiner Bound: niminal nuestcate connet fall co ond linit (B abulity
to stimalate ecunomy during diep rearssions a deflatiomory trup
•Fixed exchonge cal: it county toe cvireacy to anathur, cobs foeus on
en eeshorge
thon slabiln
Constaint within the modt:. Plprmeg soply sicde censtrant-objectn eadef
betheen y and a thal 1B must acupt in shode
Polin fargel lyt, 1) assume ут=уea
, Date.
=7 Monetary Rull Curve(MR)
カ
- MR shers the optimal output cinllatin combrotien for any DC CB tou
PCCが²=ろ)
A Pしもれとって) •Slep Finding tongencins
ก2 Por any given PC, the CB lools fur the poird
thwt touchesits smallist possibu loss crde
MR
This represents the min loss achied guen the
supply side constraint
StpJoining tongencios
By cwnructng thest optimal ponts CA,B,C)
across voorlous Pc, we derive MK
Cudjuslm.r pulh)
•The MR curve reprisents the path alory which Cs
will steer the economy back to Bliss Poid
following shock
-2t B is zero, thi MR curd is vertica!
24 B is verg high, the MR cune is flatur
- DerNution ot MR equatin
(= (ge-y?)2 1 BCHC- TJ o st. Ti= 1 t aC ye-gen)
カンTレール
He Hetalyeyea) @
Eay ,nte
しこしgビーサィa」² BCしARしりでDen) 毎が
dL
1= 2lye=yea) +2B [ Te-1 t alye-yz) -7'](x) =0
lge- yeu) = -2df [e -7= # (B7)
lyt-yeq) =-aB Cte - 1) -MR lu
• Negatid sign indiictes that it ratlatica uboe torent b 7tt) thi сB
must cnate a negutice output gop lye cyea) to bring it dion
• a: it PL is stuep Chighd), a smaller ontput gap midect to
achikt specitic redactua inintletua
B: it CB is higklyintletion uvese (hgh B), it will chrosea
larger putput gep to hit the intlaten tengat fastere
