Upload
lymien
View
216
Download
0
Embed Size (px)
Citation preview
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheMonetaryApproachtoInterna8onal
MacroeconomicsProfessorGeorgeAlogoskoufis
AthensUniversityofEconomicsandBusiness
1
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheMonetaryApproach• The monetary approach is one of the central pillars of international
macroeconomics. Its point of departure is the so called monetary model, which identifies the factors affecting long-term nominal exchange rates. The monetary model was originally used as a framework of analysis of the balance of payments in a fixed exchange rate regime (Frenkel and Johnson 1976), and then as a framework for analysis of the determination of nominal exchange rates in a flexible exchange rate regime (Frenkel and Johnson 1978).
• The basic monetary approach assumes that there is full flexibility in prices and focuses on the equilibrium conditions in the money market and the international foreign exchange markets. Although this is basically an ad hoc model, like the Mundell-Fleming model, many of its theoretical properties are confirmed by inter-temporal optimization models in monetary economies (see Lucas 1982).
2
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
PurchasingPowerParity• A key component of the monetary approach is the concept of
purchasing power parity. The idea originated from the early 19th century, and one can find it in the writings of Ricardo. The idea was revived in the early 20th century by Cassel (1921).
• The approach of Cassel starts with the observation that the exchange rate is the relative price of two currencies. Since the purchasing power of the domestic currency is 1/P, where P is the domestic price level and the purchasing power of the foreign currency is 1/P*, where P* is the foreign price level, the relative price of two currencies should reflect their relative purchasing power. In this case, it should follow that,
3
S = P / P* s = p − p*
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
PurchasingPowerParityandtheISCurve
ThetheoryofpurchasingpowerparitycanbederivedfromtheIScurveofanopeneconomy,whentheelas8cityofaggregatedemandwithrespecttotherealexchangeratetendstoinfinity.
Asδtendstoinfinity,aggregatedemandwillbefiniteonlyifthelogarithmoftherealexchangerates+p*-ptendstozero,thatisifpurchasingpowerparityissa8sfied.
Iftheelas8cityofaggregatedemandwithrespecttotherealexchangerateisveryhigh,thentherecannotbelargedevia8onsbetweendomes8candinterna8onalprices,expressedinacommoncurrency,asevensmalldevia8onswouldproducelargechangesinaggregatedemand.Effec8vely,thetheoryofpurchasingpowerparityassertsthatdomes8candforeigngoodsareperfectsubs8tutes.
4
y = δ (s + p*− p)+ γ y −σ i + g
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
ThePurchasingPowerParityApproach
• Thepurchasingpowertheoryapproachessen8allyrequiresthattherealexchangerateshouldbeconstant.However,thispredic8onisgenerallyrejectedbyempiricalevidence.Realexchangeratesarenotconstant,butdisplayconsiderablefluctua8ons.Moreover,thereseemstobeastrongposi8vecorrela8onbetweennominalandrealexchangerates,whichisnotconsistentwithpurchasingpowerparity.
• Avariantofthisapproach,whichwewillexaminebelow,allowsfluctua8onsintherealexchangerateandtreatspurchasingpowerparityasatheorydeterminingthelong-termrealexchangerate.
• Inanycase,forthemonetarymodelwithfullyflexibleprices,theassump8onofpurchasingpowerparityiscentral.
5
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheMonetaryApproachtotheBalanceofPayments
• Themonetaryapproachtothebalanceofpayments(FrenkelandJohnson1976),usesthemonetarymodeltoexplainthebehaviorofthebalanceofpayments,underaregimeoffixedexchangerates.
• Considerasmallopeneconomythatmaintainsaconstantexchangeratethroughinterven8onsofitscentralbankintheforeignexchangemarket.
• Themoneysupplyisdeterminedby,
6
M = µB = µ(Bf + Bd )
• whereΜdenotesthemoneysupply,Bthemonetarybase(highpoweredmoney),μthemul8plierofthemonetarybase,Bfnetforeignexchangereservesofthecentralbank,andBdnetdomes8ccreditofthecentralbanktothepublicandthebankingsystem.
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
EquilibriumintheMoneyMarketunderFixedExchangeRates
7
m = θbf + (1−θ )bd
m − p = φy − λi
i = i*
s_= p − p*
m = s_+ p*+φy − λi*
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
MainPredic8onsoftheMonetaryApproachtotheBalanceofPayments
• Adevalua8on(increaseins),ariseintheinterna8onalpricelevel,anincreaseindomes8coutputandincomeandareduc8onininterna8onalnominalinterestrates,increasethedemandformoney,and,forgivendomes8ccredit,causeincreasesinforeignreserves.Theincreaseinforeignexchangereserveswilloccurthroughsurplusesinthebalanceofpayments.
• Ontheotherhand,ifthereisanexpansionindomes8ccreditexpansion,theonlyresultwillbealossofnetforeignexchangereserves,asthedemandformoneywillnotchange.Thus,adomes8ccreditexpansionwillcauseadeficitinthebalanceofpayments.
8
bf =1θ
s_+ p*+φy − λi*−(1−θ )bd
⎡⎣⎢
⎤⎦⎥
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheConceptoftheBalanceofPaymentsRelevantfortheMonetaryApproach
• Themonetaryapproachtothebalanceofpaymentsisnotconcernedwiththedetermina8onofthecurrentaccount,buttheso-calledofficialbalance.
• Officialbalanceisnoneotherthanthesumofthecurrentaccountandthecapitalaccount,withouttakingaccountofchangesinthenetforeignexchangereservesofthecentralbank.
• Onecouldcallthemonetaryapproachasthemonetaryapproachtothechangeinforeignexchangereservesofthecentralbank.
9
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheMonetaryApproachtoFlexibleExchangeRates
10
i = i*+ se•
m − p = φy − λi
s = p − p*
se•
= 1λs −m +φy − λi*+ p*( )
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
MainPredic8onsoftheMonetaryApproachtotheExchangeRate
• Increasesindomes8cmoneysupplyandinterna8onalinterestratescauseadeprecia8onofthenominalexchangerate
• Increasesindomes8cincomeandtheinterna8onalpricelevelcauseanapprecia8onofthenominalexchangerate.
• Inanequilibriumwithout"bubbles"therecanbenoexpecta8onsoffuturechangesintheexchangerate.Theexchangerate,asanon-predefinedvariable,immediatelyadjuststothesteadystateequilibrium
11
s = m −φy + λi*− p*
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheMonetaryApproachandRealExchangeRates
• Itrequiresthattherealexchangerateisconstant,andthataslongasdomes8cinfla8ondiffersfrominterna8onalinfla8ontherewillbeacon8nuousadjustmentoftheexchangerate,inordertosa8sfythepurchasingpowerparitycondi8on.
• However,empirically,purchasingpowerparitydoesnotappeartobevalid.
• Realexchangeratesfluctuate,andtheirfluctua8onsarecloselyrelatedtofluctua8onsinnominalexchangerates.
• Avariantofthemonetarymodel,combinesitwiththeassump8onofthegradualadjustmentofthepricelevelinordertoachievepurchasingpowerparityinthesteadystate.Thus,theassump8onofpurchasingpowerparityisonlyassumedtoholdinthesteadystateandnotintheshortrun.
12
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
GradualAdjustmentofthePriceLevel
• Suppose,onthelinesoftheDornbusch(1976)model,thatthedomes8cpriceleveladjustsgraduallytowardsitssteadystateequilibriumlevel,whichisconsideredtobethepricelevelthatsa8sfiespurchasingpowerparity.
13
p•= π (s + p*− p)
• π>0isaparameterdeno8ngthespeedofadjustmentofthedomes8cpriceleveltowardsitssteadystateequilibrium,definedaspurchasingpowerparity.
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheMonetaryModelwithGradualPriceAdjustment
Asthedomes8cpricelevelisapredeterminedvariable,andcannotadjustintheshortruntoequilibratethedomes8cmoneymarket,thisrolemustbeplayedbythedomes8cnominalinterestrate.Sincethedomes8cnominalinterestratecanonlydifferfromtheinterna8onalnominalinterestratetotheextentthatthereareexpecta8onsoffuturechangesintheexchangerate,theexpectedandactualchangeintheexchangeratemustbesuchastomaintainequilibriuminthedomes8cmoneymarket.
14
p•= π (s + p*− p)
s•= se
•
= 1λ
p −m +φy − λi*( )
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheMonetaryApproachwithGradualAdjustmentofthePriceLevel
15
p
s
s=0 p=0
E
45ºp* pE
sE
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
APermanentIncreaseintheDomes8cMoneySupply
16
p
s
s=0 p=0
E
45ºp*
E'
E0
pE pE'
sE
s0
sE'
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheDynamicPathoftheNominalExchangeRate,thePriceLevelandtheDomes8cNominal
InterestRate
17
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheDynamicPathoftheNominalandtheRealExchangeRate
18
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
APermanentIncreaseintheInterna8onalPriceLevel
20
p
s
s=0 p=0
E
45ºp*
E'
pE
sE
sE'
p*'
p*
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheMonetaryApproachtotheExchangeRateinDiscreteTime
Themonetarymodelcaneasilybyadaptedtoaaccommodatediscrete8meandstochas8cshocks.Astochas8cversionofthemonetarymodeltakesthefollowingform,
21
mt − pt = φyt − λit
it = it* + Etst+1 − st
pt = st + pt*
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheDetermina8onoftheNominalExchangeRate
Usingthemodeltoeliminatetheothertwoendogenousvariables,iandp,theexchangerateisdeterminedby,
22
st =λ1+ λ
Etst+1 +1
1+ λ(mt −φyt + λit
* − pt*)
Thecurrentnominalexchangerateisaweightedaverageoftheexpectedfuturenominalexchangerate,andthesocalledfundamentalsf,whichinthecaseofthemonetarymodelaretheexogenousvariablesthataffectthedomes8cmoneymarket.Thesearethedomes8cmoneysupplym,fullemploymentoutputy,theinterna8onalnominalinterestratei*andtheinterna8onalpricelevelp*.
ft = mt −φyt + λit* − pt
*
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheRa8onalExpecta8onsSolu8onfortheNominalExchangeRate
Throughsuccessivesubs8tu8ons,wegetthatthera8onalexpecta8onssolu8onfortheexchangeratemustsa8sfy,
23
st =1
1+ λλ1+ λ
⎛⎝⎜
⎞⎠⎟i=0
k∑i
Et mt+i −φyt+i + λit+i* − pt+i
*( )+ λ1+ λ
⎛⎝⎜
⎞⎠⎟k+1
Etst+k+1
Ifexpecta8onsaboutthefutureevolu8onoftheexchangerategrowataratewhichdoesnotexceed1/λ,then,itfollowsthat,
limk→∞
λ1+ λ
⎛⎝⎜
⎞⎠⎟k+1
Etst+k+1 = 0
Thiscondi8oniscalledatransversalitycondi'on,andessen8allyprecludesexplosiveexpecta8onsaboutthefutureevolu8onoftheexchangerate.
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheFundamentalSolu8onfortheExchangeRate
Takingthelimitofthesolu8on,asktendstoinfinity,andusingthetransversalitycondi8on,thera'onalexpecta'onsequilibriumsolu'onfortheexchangeratecanbewrigenas,
24
st =1
1+ λEt
λ1+ λ
⎛⎝⎜
⎞⎠⎟i=0
∞∑i
mt+i −φyt+i + λit+i* − pt+i
*( ) = 11+ λ
λ1+ λ
⎛⎝⎜
⎞⎠⎟i=0
∞∑i
Et ft+i
Thisisthesocalledfundamentalsolu'onfortheexchangerate,asitdependsonlyontheexpectedfutureevolu8onofthefundamentalsofthedomes8cmoneymarket.
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
Proper8esoftheFundamentalSolu8on
Asanassetprice,theexchangerateadjuststoequilibratethedomes8cmoneymarket,throughitseffectsonthedomes8cpricelevelandthedomes8cnominalinterestrate.
Becauseofuncoveredinterestparity,thecurrentequilibriumnominalexchangeratedependsontheexpectedfutureexchangerate.Thus,thecurrentexchangeratedependsontheexpectedfutureevolu8onofallexogenousvariablesthataffectthedomes8cmoneymarket,suchasthedomes'cmoneysupply,fullemploymentoutput(whichaffectsmoneydemand),interna'onalnominalinterestrates(whichaffectdomes8cnominalinterestratesandhencemoneydemand),andtheinterna'onalpricelevel(whichaffectsthedomes8cpricelevelandhencemoneydemand).
25
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
Expecta8onsand“Bubbles”fortheExchangeRate
Thefundamentalsolu8onisnottheonlysolu8on.Amoregeneralsolu8onwouldtaketheform,
26
st =1
1+ λλ1+ λ
⎛⎝⎜
⎞⎠⎟i=0
∞∑i
Et ft+i + zt
wherezisanextraneousvariable,followingastochas8cprocessdefinedby,
zt =1+ λλ
zt−1 + ε tz
whereεzisawhitenoiseprocess,withzeromeanandconstantvariance.zis
anexplosivestochas8cprocess,andisojenreferredtoasabubble.Iftheexchangeratedependsonabubble,thenthebubblewilleventuallydominateitsbehavior,andthepathoftheexchangeratewillbeexplosive.
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
ClosedFormSolu8onsfortheExchangeRate:FundamentalsfollowaSta8onaryAR(1)Process
Inordertosaymoreaboutexchangeratedetermina8oninthemonetarymodel,weneedtomakeassump8onsabouttheexogenousprocessesdrivingthefundamentals.
Letusini8allyassumethethefundamentalsfollowasta8onaryAR(1)process,aroundaconstantmean.Thus,thefundamentalsareassumedtofollow,
27
ft = (1− ρ) f0 + ρ ft−1 + ε tf
Thekperiodaheadpredictor,i.ethera8onalexpecta8onabouttheirvaluekperiodsahead,dependsonlyonthecurrentfundamentals,accordingto,
Et ft+i = (1− ρ i ) f0 + ρ i ft
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheMeanandVarianceoftheExchangeRate
Subs8tu8nginthefundamentalsolu8on,theclosedformsolu8ontakestheform,
28
st = f0 +1
1+ λ(1− ρ)ft − f0( )
Themeanoftheexchangerateisequaltothemeanofthefundamentals,andthecurrentexchangeratedependsonthedevia8onofthecurrentfundamentalsfromtheirmean.Theresponseofthenominalexchangeratetodevia8onsofthecurrentfundamentalsfromtheirmeanislessthanonetoone,sinceλisposi8ve.Thus,thevarianceofthenominalexchangeratewillbelowerthanthevarianceofthefundamentals.
Var(st ) =1
1+ λ(1− ρ)⎛⎝⎜
⎞⎠⎟
2
Var( ft ) <Var( ft )
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheFundamentalsFollowaNon-Sta8onaryProcess
Letusalterna8velyassumethatthefundamentalsfollowanintegratedAR(1)process,i.ethatthechangeinthefundamentalsfollowsanAR(1)process.Thisprocesstakestheform,
29
Δft = ρΔft−1 + ε tf
Undersuchaprocess,thekperiodaheadpredictorofthefundamentalsandtheclosedformsolu8onfortheexchangeratetaketheform,
Et ft+k = ft + ρ iΔft = ft +1− ρ k
1− ρ⎛⎝⎜
⎞⎠⎟i=1
k∑ ρΔft
st = ft +λρ
1+ λ(1− ρ)Δft
GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016
TheChangeintheExchangeRateanditsVariance
Thefirstdifferenceinthenominalexchangerateissta8onary,andfollows,
30
Δst =1+ λ
1+ λ(1− ρ)Δft −
λρ1+ λ(1− ρ)
Δft−1
Ajersomealgebra,onefindsthat,
Var(Δst ) = 1+ 2(1− ρ)(1+ λ)λρ1+ λ(1− ρ)( )2
⎛
⎝⎜⎞
⎠⎟Var(Δft ) >Var(Δft )
IfthefundamentalsfollowanintegratedAR(1)processthenthemonetarymodelcanpoten8allyexplaintheexcessvola8lityofnominalexchangerates.However,itcannotexplainfluctua8onsintherealexchangerate,norcanitaccountforthehighposi8vecorrela8onoffluctua8onsinnominalandrealexchangerates.