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The Monetary Approach toInterna8onalMacroeconomicsProfessor George AlogoskouﬁsAthens University of Economics and BusinessGeorge Alogoskouﬁs, Interna'onal Macroeconomics, 20161

The Monetary Approach The monetary approach is one of the central pillars of internationalmacroeconomics. Its point of departure is the so called monetarymodel, which identifies the factors affecting long-term nominalexchange rates. The monetary model was originally used as aframework of analysis of the balance of payments in a fixedexchange rate regime (Frenkel and Johnson 1976), and then as aframework for analysis of the determination of nominal exchangerates in a flexible exchange rate regime (Frenkel and Johnson 1978). The basic monetary approach assumes that there is full flexibility inprices and focuses on the equilibrium conditions in the money marketand the international foreign exchange markets. Although this isbasically an ad hoc model, like the Mundell-Fleming model, many ofits theoretical properties are confirmed by inter-temporal optimizationmodels in monetary economies (see Lucas 1982).George Alogoskouﬁs, Interna'onal Macroeconomics, 20162

Purchasing Power Parity A key component of the monetary approach is the concept ofpurchasing power parity. The idea originated from the early 19thcentury, and one can find it in the writings of Ricardo. The idea wasrevived in the early 20th century by Cassel (1921). The approach of Cassel starts with the observation that the exchangerate is the relative price of two currencies. Since the purchasing powerof the domestic currency is 1/P, where P is the domestic price level andthe purchasing power of the foreign currency is 1/P*, where P* is theforeign price level, the relative price of two currencies should reflecttheir relative purchasing power. In this case, it should follow that,S P /P*George Alogoskouﬁs, Interna'onal Macroeconomics, 2016s p p*3

Purchasing Power Parity and theIS Curvey δ (s p * p) γ y σ i gThe theory of purchasing power parity can be derived from the IS curve of an openeconomy, when the elas8city of aggregate demand with respect to the real exchangerate tends to inﬁnity.As δ tends to inﬁnity, aggregate demand will be ﬁnite only if the logarithm of the realexchange rate s p*-p tends to zero, that is if purchasing power parity is sa8sﬁed.If the elas8city of aggregate demand with respect to the real exchange rate is veryhigh, then there cannot be large devia8ons between domes8c and interna8onalprices, expressed in a common currency, as even small devia8ons would producelarge changes in aggregate demand. Eﬀec8vely, the theory of purchasing powerparity asserts that domes8c and foreign goods are perfect subs8tutes.George Alogoskouﬁs, Interna'onal Macroeconomics, 20164

The Purchasing Power ParityApproach The purchasing power theory approach essen8ally requires that thereal exchange rate should be constant. However, this predic8on isgenerally rejected by empirical evidence. Real exchange rates are notconstant, but display considerable ﬂuctua8ons. Moreover, thereseems to be a strong posi8ve correla8on between nominal and realexchange rates, which is not consistent with purchasing power parity. A variant of this approach, which we will examine below, allowsﬂuctua8ons in the real exchange rate and treats purchasing powerparity as a theory determining the long-term real exchange rate. In any case, for the monetary model with fully ﬂexible prices, theassump8on of purchasing power parity is central.George Alogoskouﬁs, Interna'onal Macroeconomics, 20165

The Monetary Approach to theBalance of Payments The monetary approach to the balance of payments (Frenkel and Johnson 1976),uses the monetary model to explain the behavior of the balance of payments,under a regime of ﬁxed exchange rates. Consider a small open economy that maintains a constant exchange rate throughinterven8ons of its central bank in the foreign exchange market. The money supply is determined by,M µ B µ (B f Bd ) where Μ denotes the money supply, B the monetary base (high poweredmoney), μ the mul8plier of the monetary base, Bf net foreign exchange reservesof the central bank, and Bd net domes8c credit of the central bank to the publicand the banking system.George Alogoskouﬁs, Interna'onal Macroeconomics, 20166

Equilibrium in the Money Marketunder Fixed Exchange Ratesm θ b f (1 θ )bdm p φ y λii i*s p p*m s p * φ y λ i *George Alogoskouﬁs, Interna'onal Macroeconomics, 20167

Main Predic8ons of the MonetaryApproach to the Balance of Payments1 bf s p * φ y λ i * (1 θ )bd θ A devalua8on (increase in s), a rise in the interna8onal price level, anincrease in domes8c output and income and a reduc8on in interna8onalnominal interest rates, increase the demand for money, and, for givendomes8c credit, cause increases in foreign reserves. The increase inforeign exchange reserves will occur through surpluses in the balance ofpayments. On the other hand, if there is an expansion in domes8c credit expansion,the only result will be a loss of net foreign exchange reserves, as thedemand for money will not change. Thus, a domes8c credit expansion willcause a deﬁcit in the balance of payments.George Alogoskouﬁs, Interna'onal Macroeconomics, 20168

The Concept of the Balance of PaymentsRelevant for the Monetary Approach The monetary approach to the balance of payments is notconcerned with the determina8on of the current account,but the so-called oﬃcial balance. Oﬃcial balance is none other than the sum of the currentaccount and the capital account, without taking account ofchanges in the net foreign exchange reserves of the centralbank. One could call the monetary approach as the monetaryapproach to the change in foreign exchange reserves of thecentral bank.George Alogoskouﬁs, Interna'onal Macroeconomics, 20169

The Monetary Approach toFlexible Exchange Ratesm p φ y λi ei i * ss p p* e1s ( s m φ y λ i * p *)λGeorge Alogoskouﬁs, Interna'onal Macroeconomics, 201610

Main Predic8ons of the MonetaryApproach to the Exchange Rates m φ y λi * p * Increases in domes8c money supply and interna8onal interestrates cause a deprecia8on of the nominal exchange rate Increases in domes8c income and the interna8onal price levelcause an apprecia8on of the nominal exchange rate. In an equilibrium without "bubbles" there can be noexpecta8ons of future changes in the exchange rate. Theexchange rate, as a non-predeﬁned variable, immediately adjuststo the steady state equilibriumGeorge Alogoskouﬁs, Interna'onal Macroeconomics, 201611

The Monetary Approach andReal Exchange Rates It requires that the real exchange rate is constant, and that as long asdomes8c inﬂa8on diﬀers from interna8onal inﬂa8on there will be acon8nuous adjustment of the exchange rate, in order to sa8sfy thepurchasing power parity condi8on. However, empirically, purchasing power parity does not appear to be valid. Real exchange rates ﬂuctuate, and their ﬂuctua8ons are closely related toﬂuctua8ons in nominal exchange rates. A variant of the monetary model, combines it with the assump8on of thegradual adjustment of the price level in order to achieve purchasing powerparity in the steady state. Thus, the assump8on of purchasing power parityis only assumed to hold in the steady state and not in the short run.George Alogoskouﬁs, Interna'onal Macroeconomics, 201612

Gradual Adjustment of the PriceLevel Suppose, on the lines of the Dornbusch (1976) model, that thedomes8c price level adjusts gradually towards its steady stateequilibrium level, which is considered to be the price level thatsa8sﬁes purchasing power parity. p π (s p * p) π 0 is a parameter deno8ng the speed of adjustment of thedomes8c price level towards its steady state equilibrium, deﬁnedas purchasing power parity.George Alogoskouﬁs, Interna'onal Macroeconomics, 201613

The Monetary Model withGradual Price Adjustment p π (s p * p) e1s s ( p m φ y λ i *)λAs the domes8c price level is a predetermined variable, and cannot adjust inthe short run to equilibrate the domes8c money market, this role must beplayed by the domes8c nominal interest rate. Since the domes8c nominalinterest rate can only diﬀer from the interna8onal nominal interest rate tothe extent that there are expecta8ons of future changes in the exchangerate, the expected and actual change in the exchange rate must be such as tomaintain equilibrium in the domes8c money market.George Alogoskouﬁs, Interna'onal Macroeconomics, 201614

sThe Monetary Approach with GradualAdjustment of the Price Levels 0p 0EsE45ºp*George Alogoskouﬁs, Interna'onal Macroeconomics, 2016pEp15

sA Permanent Increase in theDomes8c Money Supplys 0p 0E0s0sE'E'EsE45ºp*George Alogoskouﬁs, Interna'onal Macroeconomics, 2016pEpE'p16

The Dynamic Path of the Nominal Exchange Rate,the Price Level and the Domes8c NominalInterest RateGeorge Alogoskouﬁs, Interna'onal Macroeconomics, 201617

The Dynamic Path of the Nominaland the Real Exchange RateGeorge Alogoskouﬁs, Interna'onal Macroeconomics, 201618

A Permanent Increase inDomes8c OutputGeorge Alogoskouﬁs, Interna'onal Macroeconomics, 201619

sA Permanent Increase in theInterna8onal Price Levels 0sEEsE'p 0p*E'45ºp*p*'George Alogoskouﬁs, Interna'onal Macroeconomics, 2016pEp20

The Monetary Approach to theExchange Rate in Discrete TimeThe monetary model can easily by adapted to a accommodate discrete8me and stochas8c shocks. A stochas8c version of the monetary modeltakes the following form,mt pt φ yt λ itit i Et st 1 st*tpt st p*tGeorge Alogoskouﬁs, Interna'onal Macroeconomics, 201621

The Determina8on of theNominal Exchange RateUsing the model to eliminate the other two endogenous variables, i and p, theexchange rate is determined by,λ1**st Et st 1 (mt φ yt λ it pt )1 λ1 λThe current nominal exchange rate is a weighted average of the expected futurenominal exchange rate, and the so called fundamentals f, which in the case of themonetary model are the exogenous variables that aﬀect the domes8c moneymarket. These are the domes8c money supply m, full employment output y, theinterna8onal nominal interest rate i* and the interna8onal price level p*.ft mt φ yt λ i p*tGeorge Alogoskouﬁs, Interna'onal Macroeconomics, 2016*t22

The Ra8onal Expecta8ons Solu8onfor the Nominal Exchange RateThrough successive subs8tu8ons, we get that the ra8onal expecta8ons solu8on forthe exchange rate must sa8sfy,k λ 1 λ **st Et mt i φ yt i λ it i pt i i 0 1 λ1 λ1 λi()k 1Et st k 1If expecta8ons about the future evolu8on of the exchange rate grow at a rate whichdoes not exceed 1/λ, then, it follows that, λ lim k 1 λ k 1Et st k 1 0This condi8on is called a transversality condi'on, and essen8ally precludesexplosive expecta8ons about the future evolu8on of the exchange rate.George Alogoskouﬁs, Interna'onal Macroeconomics, 201623

The Fundamental Solu8on forthe Exchange RateTaking the limit of the solu8on, as k tends to inﬁnity, and using the transversalitycondi8on, the ra'onal expecta'ons equilibrium solu'on for the exchange ratecan be wrigen as, λ λ 11**st Et i 0 mt i φ yt i λ it i pt i Et ft i i 0 1 λ 1 λ 1 λ1 λi()iThis is the so called fundamental solu'on for the exchange rate, as it dependsonly on the expected future evolu8on of the fundamentals of the domes8cmoney market.George Alogoskouﬁs, Interna'onal Macroeconomics, 201624

Proper8es of the FundamentalSolu8onAs an asset price, the exchange rate adjusts to equilibrate thedomes8c money market, through its eﬀects on the domes8c pricelevel and the domes8c nominal interest rate.Because of uncovered interest parity, the current equilibriumnominal exchange rate depends on the expected future exchangerate. Thus, the current exchange rate depends on the expectedfuture evolu8on of all exogenous variables that aﬀect the domes8cmoney market, such as the domes'c money supply, full employmentoutput (which aﬀects money demand), interna'onal nominal interestrates (which aﬀect domes8c nominal interest rates and hence moneydemand), and the interna'onal price level (which aﬀects thedomes8c price level and hence money demand).George Alogoskouﬁs, Interna'onal Macroeconomics, 201625

Expecta8ons and “Bubbles” forthe Exchange RateThe fundamental solu8on is not the only solu8on. A more general solu8on wouldtake the form, λ 1st Ef z tt iti 0 1 λ1 λiwhere z is an extraneous variable, following a stochas8c process deﬁned by,1 λzt zt 1 ε tzλzwhere ε is a white noise process, with zero mean and constant variance. z isan explosive stochas8c process, and is ojen referred to as a bubble. If theexchange rate depends on a bubble, then the bubble will eventuallydominate its behavior, and the path of the exchange rate will be explosive.George Alogoskouﬁs, Interna'onal Macroeconomics, 201626

Closed Form Solu8ons for the Exchange Rate:Fundamentals follow a Sta8onary AR(1) ProcessIn order to say more about exchange rate determina8on in the monetary model, weneed to make assump8ons about the exogenous processes driving the fundamentals.Let us ini8ally assume the the fundamentals follow a sta8onary AR(1) process,around a constant mean. Thus, the fundamentals are assumed to follow,ft (1 ρ ) f0 ρ ft 1 ε tfThe k period ahead predictor, i.e the ra8onal expecta8on about their value kperiods ahead, depends only on the current fundamentals, according to,Et ft i (1 ρ i ) f0 ρ i ftGeorge Alogoskouﬁs, Interna'onal Macroeconomics, 201627

The Mean and Variance of theExchange RateSubs8tu8ng in the fundamental solu8on, the closed form solu8on takesthe form,1st f0 ft f0 )(1 λ (1 ρ )The mean of the exchange rate is equal to the mean of the fundamentals,and the current exchange rate depends on the devia8on of the currentfundamentals from their mean. The response of the nominal exchangerate to devia8ons of the current fundamentals from their mean is lessthan one to one, since λ is posi8ve. Thus, the variance of the nominalexchange rate will be lower than the variance of the fundamentals.2 1Var(st ) Var( ft ) Var( ft ) 1 λ (1 ρ ) George Alogoskouﬁs, Interna'onal Macroeconomics, 201628

The Fundamentals Follow a NonSta8onary ProcessLet us alterna8vely assume that the fundamentals follow an integrated AR(1)process, i.e that the change in the fundamentals follows an AR(1) process. Thisprocess takes the form,Δft ρΔft 1 ε tfUnder such a process, the k period ahead predictor of the fundamentals and theclosed form solu8on for the exchange rate take the form,Et ft kk 1 ρ i ft i 1 ρ Δft ft ρΔft 1 ρ kλρst ft Δft1 λ (1 ρ )George Alogoskouﬁs, Interna'onal Macroeconomics, 201629

The Change in the ExchangeRate and its VarianceThe ﬁrst diﬀerence in the nominal exchange rate is sta8onary, and follows,1 λλρΔst Δft Δft 11 λ (1 ρ )1 λ (1 ρ )Ajer some algebra, one ﬁnds that, 2(1 ρ )(1 λ )λρ Var(Δst ) 1 2 Var(Δft ) Var(Δft )(1 λ (1 ρ )) If the fundamentals follow an integrated AR(1) process then the monetarymodel can poten8ally explain the excess vola8lity of nominal exchange rates.However, it cannot explain ﬂuctua8ons in the real exchange rate, nor can itaccount for the high posi8ve correla8on of ﬂuctua8ons in nominal and realexchange rates.George Alogoskouﬁs, Interna'onal Macroeconomics, 201630

The Monetary Approach 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 analy

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