The Monetary Approach to Interna8onal Macroeconomics · George Alogoskouﬁs, Interna’onal Macroeconomics, 2016 The Monetary Approach to Interna8onal Macroeconomics Professor George

GeorgeAlogoskoufis,Interna'onalMacroeconomics,2016

TheMonetaryApproachtoInterna8onal

MacroeconomicsProfessorGeorgeAlogoskoufis

AthensUniversityofEconomicsandBusiness

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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).

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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,

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S = P / P* s = p − p*


PurchasingPowerParityandtheISCurve

ThetheoryofpurchasingpowerparitycanbederivedfromtheIScurveofanopeneconomy,whentheelas8cityofaggregatedemandwithrespecttotherealexchangeratetendstoinfinity.

Asδtendstoinfinity,aggregatedemandwillbefiniteonlyifthelogarithmoftherealexchangerates+p*-ptendstozero,thatisifpurchasingpowerparityissa8sfied.

Iftheelas8cityofaggregatedemandwithrespecttotherealexchangerateisveryhigh,thentherecannotbelargedevia8onsbetweendomes8candinterna8onalprices,expressedinacommoncurrency,asevensmalldevia8onswouldproducelargechangesinaggregatedemand.Effec8vely,thetheoryofpurchasingpowerparityassertsthatdomes8candforeigngoodsareperfectsubs8tutes.

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y = δ (s + p*− p)+ γ y −σ i + g


ThePurchasingPowerParityApproach

• Thepurchasingpowertheoryapproachessen8allyrequiresthattherealexchangerateshouldbeconstant.However,thispredic8onisgenerallyrejectedbyempiricalevidence.Realexchangeratesarenotconstant,butdisplayconsiderablefluctua8ons.Moreover,thereseemstobeastrongposi8vecorrela8onbetweennominalandrealexchangerates,whichisnotconsistentwithpurchasingpowerparity.

• Avariantofthisapproach,whichwewillexaminebelow,allowsfluctua8onsintherealexchangerateandtreatspurchasingpowerparityasatheorydeterminingthelong-termrealexchangerate.

• Inanycase,forthemonetarymodelwithfullyflexibleprices,theassump8onofpurchasingpowerparityiscentral.

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TheMonetaryApproachtotheBalanceofPayments

• Themonetaryapproachtothebalanceofpayments(FrenkelandJohnson1976),usesthemonetarymodeltoexplainthebehaviorofthebalanceofpayments,underaregimeoffixedexchangerates.

• Considerasmallopeneconomythatmaintainsaconstantexchangeratethroughinterven8onsofitscentralbankintheforeignexchangemarket.

• Themoneysupplyisdeterminedby,

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M = µB = µ(Bf + Bd )

• whereΜdenotesthemoneysupply,Bthemonetarybase(highpoweredmoney),μthemul8plierofthemonetarybase,Bfnetforeignexchangereservesofthecentralbank,andBdnetdomes8ccreditofthecentralbanktothepublicandthebankingsystem.


EquilibriumintheMoneyMarketunderFixedExchangeRates

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m = θbf + (1−θ )bd

m − p = φy − λi

i = i*

s_= p − p*

m = s_+ p*+φy − λi*


MainPredic8onsoftheMonetaryApproachtotheBalanceofPayments

• Adevalua8on(increaseins),ariseintheinterna8onalpricelevel,anincreaseindomes8coutputandincomeandareduc8onininterna8onalnominalinterestrates,increasethedemandformoney,and,forgivendomes8ccredit,causeincreasesinforeignreserves.Theincreaseinforeignexchangereserveswilloccurthroughsurplusesinthebalanceofpayments.

• Ontheotherhand,ifthereisanexpansionindomes8ccreditexpansion,theonlyresultwillbealossofnetforeignexchangereserves,asthedemandformoneywillnotchange.Thus,adomes8ccreditexpansionwillcauseadeficitinthebalanceofpayments.

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bf =1θ

s_+ p*+φy − λi*−(1−θ )bd

⎡⎣⎢

⎤⎦⎥


TheConceptoftheBalanceofPaymentsRelevantfortheMonetaryApproach

• Themonetaryapproachtothebalanceofpaymentsisnotconcernedwiththedetermina8onofthecurrentaccount,buttheso-calledofficialbalance.

• Officialbalanceisnoneotherthanthesumofthecurrentaccountandthecapitalaccount,withouttakingaccountofchangesinthenetforeignexchangereservesofthecentralbank.

• Onecouldcallthemonetaryapproachasthemonetaryapproachtothechangeinforeignexchangereservesofthecentralbank.

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TheMonetaryApproachtoFlexibleExchangeRates

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i = i*+ se•

m − p = φy − λi

s = p − p*

se•

= 1λs −m +φy − λi*+ p*( )


MainPredic8onsoftheMonetaryApproachtotheExchangeRate

• Increasesindomes8cmoneysupplyandinterna8onalinterestratescauseadeprecia8onofthenominalexchangerate

• Increasesindomes8cincomeandtheinterna8onalpricelevelcauseanapprecia8onofthenominalexchangerate.

• Inanequilibriumwithout"bubbles"therecanbenoexpecta8onsoffuturechangesintheexchangerate.Theexchangerate,asanon-predefinedvariable,immediatelyadjuststothesteadystateequilibrium

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s = m −φy + λi*− p*


TheMonetaryApproachandRealExchangeRates

• Itrequiresthattherealexchangerateisconstant,andthataslongasdomes8cinfla8ondiffersfrominterna8onalinfla8ontherewillbeacon8nuousadjustmentoftheexchangerate,inordertosa8sfythepurchasingpowerparitycondi8on.

• However,empirically,purchasingpowerparitydoesnotappeartobevalid.

• Realexchangeratesfluctuate,andtheirfluctua8onsarecloselyrelatedtofluctua8onsinnominalexchangerates.

• Avariantofthemonetarymodel,combinesitwiththeassump8onofthegradualadjustmentofthepricelevelinordertoachievepurchasingpowerparityinthesteadystate.Thus,theassump8onofpurchasingpowerparityisonlyassumedtoholdinthesteadystateandnotintheshortrun.

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GradualAdjustmentofthePriceLevel

• Suppose,onthelinesoftheDornbusch(1976)model,thatthedomes8cpriceleveladjustsgraduallytowardsitssteadystateequilibriumlevel,whichisconsideredtobethepricelevelthatsa8sfiespurchasingpowerparity.

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p•= π (s + p*− p)

• π>0isaparameterdeno8ngthespeedofadjustmentofthedomes8cpriceleveltowardsitssteadystateequilibrium,definedaspurchasingpowerparity.


TheMonetaryModelwithGradualPriceAdjustment

Asthedomes8cpricelevelisapredeterminedvariable,andcannotadjustintheshortruntoequilibratethedomes8cmoneymarket,thisrolemustbeplayedbythedomes8cnominalinterestrate.Sincethedomes8cnominalinterestratecanonlydifferfromtheinterna8onalnominalinterestratetotheextentthatthereareexpecta8onsoffuturechangesintheexchangerate,theexpectedandactualchangeintheexchangeratemustbesuchastomaintainequilibriuminthedomes8cmoneymarket.

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p•= π (s + p*− p)

s•= se

•

= 1λ

p −m +φy − λi*( )


TheMonetaryApproachwithGradualAdjustmentofthePriceLevel

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p

s

s=0 p=0

E

45ºp* pE

sE


APermanentIncreaseintheDomes8cMoneySupply

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p

s

s=0 p=0

E

45ºp*

E'

E0

pE pE'

sE

s0

sE'


TheDynamicPathoftheNominalExchangeRate,thePriceLevelandtheDomes8cNominal

InterestRate

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TheDynamicPathoftheNominalandtheRealExchangeRate

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APermanentIncreaseinDomes8cOutput

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APermanentIncreaseintheInterna8onalPriceLevel

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p

s

s=0 p=0

E

45ºp*

E'

pE

sE

sE'

p*'

p*


TheMonetaryApproachtotheExchangeRateinDiscreteTime

Themonetarymodelcaneasilybyadaptedtoaaccommodatediscrete8meandstochas8cshocks.Astochas8cversionofthemonetarymodeltakesthefollowingform,

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mt − pt = φyt − λit

it = it* + Etst+1 − st

pt = st + pt*


TheDetermina8onoftheNominalExchangeRate

Usingthemodeltoeliminatetheothertwoendogenousvariables,iandp,theexchangerateisdeterminedby,

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st =λ1+ λ

Etst+1 +1

1+ λ(mt −φyt + λit

* − pt*)

Thecurrentnominalexchangerateisaweightedaverageoftheexpectedfuturenominalexchangerate,andthesocalledfundamentalsf,whichinthecaseofthemonetarymodelaretheexogenousvariablesthataffectthedomes8cmoneymarket.Thesearethedomes8cmoneysupplym,fullemploymentoutputy,theinterna8onalnominalinterestratei*andtheinterna8onalpricelevelp*.

ft = mt −φyt + λit* − pt

*


TheRa8onalExpecta8onsSolu8onfortheNominalExchangeRate

Throughsuccessivesubs8tu8ons,wegetthatthera8onalexpecta8onssolu8onfortheexchangeratemustsa8sfy,

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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.


TheFundamentalSolu8onfortheExchangeRate

Takingthelimitofthesolu8on,asktendstoinfinity,andusingthetransversalitycondi8on,thera'onalexpecta'onsequilibriumsolu'onfortheexchangeratecanbewrigenas,

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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.


Proper8esoftheFundamentalSolu8on

Asanassetprice,theexchangerateadjuststoequilibratethedomes8cmoneymarket,throughitseffectsonthedomes8cpricelevelandthedomes8cnominalinterestrate.

Becauseofuncoveredinterestparity,thecurrentequilibriumnominalexchangeratedependsontheexpectedfutureexchangerate.Thus,thecurrentexchangeratedependsontheexpectedfutureevolu8onofallexogenousvariablesthataffectthedomes8cmoneymarket,suchasthedomes'cmoneysupply,fullemploymentoutput(whichaffectsmoneydemand),interna'onalnominalinterestrates(whichaffectdomes8cnominalinterestratesandhencemoneydemand),andtheinterna'onalpricelevel(whichaffectsthedomes8cpricelevelandhencemoneydemand).

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Expecta8onsand“Bubbles”fortheExchangeRate

Thefundamentalsolu8onisnottheonlysolu8on.Amoregeneralsolu8onwouldtaketheform,

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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.


ClosedFormSolu8onsfortheExchangeRate:FundamentalsfollowaSta8onaryAR(1)Process

Inordertosaymoreaboutexchangeratedetermina8oninthemonetarymodel,weneedtomakeassump8onsabouttheexogenousprocessesdrivingthefundamentals.

Letusini8allyassumethethefundamentalsfollowasta8onaryAR(1)process,aroundaconstantmean.Thus,thefundamentalsareassumedtofollow,

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ft = (1− ρ) f0 + ρ ft−1 + ε tf

Thekperiodaheadpredictor,i.ethera8onalexpecta8onabouttheirvaluekperiodsahead,dependsonlyonthecurrentfundamentals,accordingto,

Et ft+i = (1− ρ i ) f0 + ρ i ft


TheMeanandVarianceoftheExchangeRate

Subs8tu8nginthefundamentalsolu8on,theclosedformsolu8ontakestheform,

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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 )


TheFundamentalsFollowaNon-Sta8onaryProcess

Letusalterna8velyassumethatthefundamentalsfollowanintegratedAR(1)process,i.ethatthechangeinthefundamentalsfollowsanAR(1)process.Thisprocesstakestheform,

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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


TheChangeintheExchangeRateanditsVariance

Thefirstdifferenceinthenominalexchangerateissta8onary,andfollows,

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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.

The Monetary Approach to Interna8onal Macroeconomics · George Alogoskouﬁs, Interna’onal Macroeconomics, 2016 The Monetary Approach to Interna8onal Macroeconomics Professor George

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