Economics of International FinanceEconomics of International FinanceEcon. 315Econ. 315

Chapter 4:Chapter 4:

Exchange Rate DeterminationExchange Rate Determination

I. Purchasing Power Parity Theory (PPP)I. Purchasing Power Parity Theory (PPP)

(1) The Law of One Price (LOOP)(1) The Law of One Price (LOOP)

the the same same good (x) in different competitive markets must good (x) in different competitive markets must sell for sell for the same pricethe same price in the absence of transportation costs and trade in the absence of transportation costs and trade barriers between these markets i.e.,barriers between these markets i.e.,

PPxx= (R) . (P= (R) . (P**xx))

(2) Absolute PPP:(2) Absolute PPP:

Is the application of the law of one price across countries for Is the application of the law of one price across countries for all all goodsgoods and services, or for representative groups (baskets) of and services, or for representative groups (baskets) of goods and services: goods and services:

P = (R) . (PP = (R) . (P**) ) R= P/P*R= P/P*

According to the equation, the equilibrium exchange rate According to the equation, the equilibrium exchange rate between two currencies equals the ratio of the price levels in the between two currencies equals the ratio of the price levels in the two nationstwo nations

If the price of a bushel of wheat in USA is $1 and in EMU area is If the price of a bushel of wheat in USA is $1 and in EMU area is €1 then the exchange rate between the two currencies is $1/€1 = €1 then the exchange rate between the two currencies is $1/€1 = 1. This is1. This is the LOOP. the LOOP.

According to LOOPAccording to LOOP (a given commodity should have the same (a given commodity should have the same price, so that the purchasing power of the two currencies is at price, so that the purchasing power of the two currencies is at parity)parity). .

If the price of the good is different (e.g., $ 0.5 in USA and $ 1.5 If the price of the good is different (e.g., $ 0.5 in USA and $ 1.5 in EMU area), firms would purchase the good in USA and resell in EMU area), firms would purchase the good in USA and resell it in EMU area. This it in EMU area. This commodity arbitragecommodity arbitrage causes the price of causes the price of wheat to be the same in the two markets (assuming no wheat to be the same in the two markets (assuming no transportation costs or subsidies ..etc). transportation costs or subsidies ..etc).

(3) Relative PPP theory(3) Relative PPP theory

ChangeChange in the exchange rate should be proportional to the in the exchange rate should be proportional to the relative change in the price levels (relative change in the price levels (inflationinflation) in the two nations ) in the two nations over the same period. over the same period.

R1 = ((pR1 = ((p11/p/p00)/(p)/(p**11/p/p**

00)).R)).R00

R1 and R0 are exchange rates in period (1) and base period (0).R1 and R0 are exchange rates in period (1) and base period (0).

Example, if R0 = $1/€1, and there is no change in the price level Example, if R0 = $1/€1, and there is no change in the price level of the EMU area, while in the US the price increases by 50% of the EMU area, while in the US the price increases by 50% the US $ should depreciate by 50% compared to the base period. the US $ should depreciate by 50% compared to the base period. [(1.5/1)/(1/1) . 1= $1.5/ € 1 (i.e. (1.5-1)/1 = 50% depreciation)][(1.5/1)/(1/1) . 1= $1.5/ € 1 (i.e. (1.5-1)/1 = 50% depreciation)]

Application: Application: BIG MAC INDEXBIG MAC INDEX

The EconomistThe Economist's Big Mac index is based on the theory of purchasing-power parity 's Big Mac index is based on the theory of purchasing-power parity (PPP), according to which exchange rates should adjust to equalise the price of a (PPP), according to which exchange rates should adjust to equalise the price of a basket of goods and services around the world. Our basket is a burger: a basket of goods and services around the world. Our basket is a burger: a McDonald’s Big Mac.McDonald’s Big Mac.The table below shows by how much, in Big Mac PPP terms, selected currencies The table below shows by how much, in Big Mac PPP terms, selected currencies were over- or undervalued at the end of January. Broadly, the pattern is such as it were over- or undervalued at the end of January. Broadly, the pattern is such as it was last spring, the previous time this table was compiled. The most overvalued was last spring, the previous time this table was compiled. The most overvalued currency is the Icelandic krona: the exchange rate that would equalise the price of currency is the Icelandic krona: the exchange rate that would equalise the price of an Icelandic Big Mac with an American one is 158 kronur to the dollar; the actual an Icelandic Big Mac with an American one is 158 kronur to the dollar; the actual rate is 68.4, making the krona 131% too dear. The most undervalued currency is the rate is 68.4, making the krona 131% too dear. The most undervalued currency is the Chinese yuan, at 56% below its PPP rate; several other Asian currencies also Chinese yuan, at 56% below its PPP rate; several other Asian currencies also appear to be 40-50% undervalued.appear to be 40-50% undervalued.The index is supposed to give a guide to the direction in which currencies should, in The index is supposed to give a guide to the direction in which currencies should, in theory, head in the long run. It is only a rough guide, because its price reflects non-theory, head in the long run. It is only a rough guide, because its price reflects non-tradable elements—such as rent and labour. For that reason, it is probably least tradable elements—such as rent and labour. For that reason, it is probably least rough when comparing countries at roughly the same stage of development. rough when comparing countries at roughly the same stage of development. Perhaps the most telling numbers in this table are therefore those for the Japanese Perhaps the most telling numbers in this table are therefore those for the Japanese yen, which is 28% undervalued against the dollar, and the euro, which is 19% yen, which is 28% undervalued against the dollar, and the euro, which is 19% overvalued. Hence European finance ministers’ beef with the low level of the yen. overvalued. Hence European finance ministers’ beef with the low level of the yen. Source: The EconomistSource: The Economist..

Empirical tests of PPP Empirical tests of PPP

1.1. PPP works well for PPP works well for highly tradedhighly traded goods, e.g., wheat and steel, but less goods, e.g., wheat and steel, but less well for well for all traded goodsall traded goods together, and not so well for together, and not so well for all goodsall goods (which includes (which includes non-tradednon-traded commodities). commodities).

2.2. PPP works reasonably well over PPP works reasonably well over very long periodsvery long periods of time, and not of time, and not well in the short run.well in the short run.

3.3. PPP works well in cases of purely PPP works well in cases of purely monetary disturbancesmonetary disturbances and in and in inflationary periodsinflationary periods, but not so well in periods of , but not so well in periods of monetary stabilitymonetary stability and not well in at all in situations of and not well in at all in situations of major structural changemajor structural change..

Reasons why PPP may fail empirically:Reasons why PPP may fail empirically:

1. Trade barriers, transportation costs, and non-tradable goods and services

2. Imperfect competition in product markets (price discrimination across markets)

3. Differences in price level measures (different “consumption baskets”)

Criticism Criticism 1.1. The prices of identical commodity baskets, when converted to a single The prices of identical commodity baskets, when converted to a single

currency, currency, differ substantiallydiffer substantially across countries. across countries.

2.2. Relative PPP is Relative PPP is more consistentmore consistent with data, but it also with data, but it also performs quite poorly performs quite poorly to predict exchange ratesto predict exchange rates (it performs better over longer time spans for most (it performs better over longer time spans for most countries –over 5-10 years).countries –over 5-10 years).

3.3. PPP gives the R that PPP gives the R that equilibrates the trade in goods and servicesequilibrates the trade in goods and services market, and market, and completely disregarding the completely disregarding the capital accountcapital account..

4.4. PPP does not take PPP does not take non-traded goods and servicesnon-traded goods and services into account. Their prices into account. Their prices are not equalized by trade. are not equalized by trade.

5.5. PPP does not take into account PPP does not take into account transportation costs or other obstructionstransportation costs or other obstructions to to the free flow of international trade.the free flow of international trade.

But we care about PPP because it occupies a central position in But we care about PPP because it occupies a central position in the monetary asset market or portfolio balance approaches to the monetary asset market or portfolio balance approaches to BOP and exchange rate determination.BOP and exchange rate determination.

II. The monetary approach to BOP and exchange ratesII. The monetary approach to BOP and exchange rates

concentrates on monetary factors to predict long-run adjustment of nominal exchange rates:concentrates on monetary factors to predict long-run adjustment of nominal exchange rates:1.1. Based on the PPP condition.Based on the PPP condition.2.2. Uses the long-run assumption of fully flexible prices.Uses the long-run assumption of fully flexible prices.3.3. Price levels adjust to equate real aggregate Price levels adjust to equate real aggregate money supplymoney supply with real aggregate with real aggregate

money demandmoney demand: :

II.A Monetary approach to BOP under II.A Monetary approach to BOP under fixed exchange ratesfixed exchange rates

The demand for money:The demand for money:

1.1. Positively related to the level of nominal incomePositively related to the level of nominal income2.2. Stable in the long run.Stable in the long run.

Md = kPYMd = kPY

Md = the quantity of money demanded.Md = the quantity of money demanded.

k = the proportion of income individuals choose to hold as money (a constant) (1/v). k = the proportion of income individuals choose to hold as money (a constant) (1/v).

v= Velocity of Money - rate at which money turns over in gross domestic transactions during v= Velocity of Money - rate at which money turns over in gross domestic transactions during a given period. The average number of times each dollar is used to conduct a given period. The average number of times each dollar is used to conduct transactions.transactions.

P = price level (Price Index)P = price level (Price Index)Y = The real level of output (income)Y = The real level of output (income)

The supply of moneyThe supply of money

Ms = m (D+F)Ms = m (D+F)

m = money multiplier (1/rrr) [we assume that it is constant]m = money multiplier (1/rrr) [we assume that it is constant]D = domestic component of the nation’s D = domestic component of the nation’s monetary basemonetary base. It is the domestic credit . It is the domestic credit

created by the nation’s monetary authorities, or the domestic assets backing the created by the nation’s monetary authorities, or the domestic assets backing the nation’s money supply. nation’s money supply.

F = international component of the F = international component of the monetary basemonetary base (international reserves of the nation, (international reserves of the nation, e.g., in US $), D+F = the monetary base. e.g., in US $), D+F = the monetary base.

Starting from the equilibrium where Starting from the equilibrium where Md = Ms (m (D+F))Md = Ms (m (D+F)), ,

Case One:Case One: an increase in an increase in MdMd can be satisfied either by: can be satisfied either by:

- an increase in D or - an increase in D or - inflow of F (BOP surplus).- inflow of F (BOP surplus).

If D does not increase, the extra demand will be satisfied by an increase in F.If D does not increase, the extra demand will be satisfied by an increase in F.

Hence, a Hence, a surplus in BOP resultssurplus in BOP results from an excess in the stock of money demanded from an excess in the stock of money demanded that is not satisfied by an increase in D. that is not satisfied by an increase in D.

Case Two:Case Two: An increase in D, and Ms in the face of unchanged Md, F flows out the nation An increase in D, and Ms in the face of unchanged Md, F flows out the nation

and leads to a and leads to a fall in F (BOP deficit).fall in F (BOP deficit).

Hence, a deficit in BOP results from an excess in Ms that is not eliminated by Hence, a deficit in BOP results from an excess in Ms that is not eliminated by the nation’s monetary authority, but is corrected by an outflow of F.the nation’s monetary authority, but is corrected by an outflow of F.

Note That:Note That:

1.1. Under fixed exchange rate the nation has Under fixed exchange rate the nation has no control over its money supplyno control over its money supply system. The size of Ms will be the one that is consistent with BOP system. The size of Ms will be the one that is consistent with BOP equilibrium.equilibrium.

2.2. The nation’s BOP surplus or deficit isThe nation’s BOP surplus or deficit is temporary temporary and and self correctingself correcting in the in the long run. long run.

3.3. After any excess demand or supply of money is eliminated through an After any excess demand or supply of money is eliminated through an inflow inflow or outflow of fundsor outflow of funds, the BOP surplus or deficit is corrected and the , the BOP surplus or deficit is corrected and the international flow of money dries up and comes to an end. international flow of money dries up and comes to an end.

e.g., if GDP increases from 1 bn, to 1.1 $ bn, if v = 5, Md will increase from e.g., if GDP increases from 1 bn, to 1.1 $ bn, if v = 5, Md will increase from 200 $ mn. to 220 $ mn. How??200 $ mn. to 220 $ mn. How??

II.B Monetary approach to BOP under II.B Monetary approach to BOP under flexible exchange ratesflexible exchange rates. .

Under flexible exchange rates, BOP is immediately corrected by Under flexible exchange rates, BOP is immediately corrected by automatic changes in exchange ratesautomatic changes in exchange rates which causes prices to change which causes prices to change without any flow of money or reserveswithout any flow of money or reserves. Here the nation retains control . Here the nation retains control over its Ms and monetary policy: over its Ms and monetary policy:

1.1. A BOP deficit (resulting from excess Ms) leads to an A BOP deficit (resulting from excess Ms) leads to an automaticautomatic depreciationdepreciation causing the prices and Md to rise sufficiently to absorb causing the prices and Md to rise sufficiently to absorb the excess Ms and eliminate the BOP deficit without a change in F. the excess Ms and eliminate the BOP deficit without a change in F.

2.2. A BOP surplus (resulting from excess Md) leads to an A BOP surplus (resulting from excess Md) leads to an appreciationappreciation causing the prices to fall and eliminate excess Md and BOP surplus causing the prices to fall and eliminate excess Md and BOP surplus without a change in F. without a change in F.

Under a flexible exchange rate system, a Under a flexible exchange rate system, a BOP disequilibrium is BOP disequilibrium is immediately corrected by an automatic change in exchange ratesimmediately corrected by an automatic change in exchange rates and and without any international flow of money or reserves. without any international flow of money or reserves.

The actual exchange value of the currency is determined by the The actual exchange value of the currency is determined by the rate of growth of money supply and real income in the nationrate of growth of money supply and real income in the nation relative to other nations.relative to other nations.

Note:Note:1.1. A currency depreciation results from excessive money growth A currency depreciation results from excessive money growth

in the nation over time. A currency appreciation results from in the nation over time. A currency appreciation results from inadequate money growth in the nation. inadequate money growth in the nation.

2.2. A nation facing greater inflationary pressures than other A nation facing greater inflationary pressures than other nations (resulting from more rapid growth in money in nations (resulting from more rapid growth in money in relation to real income and demand for money) will find its relation to real income and demand for money) will find its exchange rate rising (exchange rate rising (aa depreciationdepreciation). ).

3.3. A country facing lower inflationary pressures than the rest of A country facing lower inflationary pressures than the rest of the world, will find its exchange rate falling (the world, will find its exchange rate falling (an an appreciationappreciation). ).

II.C Managed floating of exchange rateII.C Managed floating of exchange rate

Under a managed floating , the authorities will intervene in foreign Under a managed floating , the authorities will intervene in foreign exchange markets and either lose or accumulate international reserves to exchange markets and either lose or accumulate international reserves to prevent an excessive depreciation or appreciation of its currency, i.e., prevent an excessive depreciation or appreciation of its currency, i.e., Under the system part of the BOP deficit is corrected by:Under the system part of the BOP deficit is corrected by:

1.1. One Part by a depreciation of the domestic currency,One Part by a depreciation of the domestic currency,

2.2. The other part is corrected by a loss of international reserves (F). The other part is corrected by a loss of international reserves (F).

The country’s money supply is also affected by Excessive or inadequate The country’s money supply is also affected by Excessive or inadequate money supply in other nations but to a smaller extent than under flexible money supply in other nations but to a smaller extent than under flexible exchange rate system.exchange rate system.

III. The monetary approach to exchange rate III. The monetary approach to exchange rate determinationdetermination

If markets are competitive and there are no tariffs, transportation costs If markets are competitive and there are no tariffs, transportation costs or other obstructions to trade, then according to LOOP the price of a or other obstructions to trade, then according to LOOP the price of a commodity must be the same in two countries.commodity must be the same in two countries.

P = R P* , then; P = R P* , then; R = P/P*R = P/P*

We can show that the exchange rate between two currencies is We can show that the exchange rate between two currencies is determined according to the monetary approach by using the determined according to the monetary approach by using the money money demand in the two nations. demand in the two nations.

Md = k PY and Md*=k *P*Y*Md = k PY and Md*=k *P*Y*

In equilibrium Md = Ms and Md* = Ms*In equilibrium Md = Ms and Md* = Ms*

Ms*/Ms = k* P*Y*/k PYMs*/Ms = k* P*Y*/k PY

Divide both sides by P*/P and Ms*/Ms , we getDivide both sides by P*/P and Ms*/Ms , we get

P/P* = Msk*Y*/Ms*kYP/P* = Msk*Y*/Ms*kY But since R=P/P* ;But since R=P/P* ;

R = Ms k*Y* / Ms* kYR = Ms k*Y* / Ms* kY

Since k*and Y* as well as k and Y are assumed constant Since k*and Y* as well as k and Y are assumed constant R is constant as long as Ms R is constant as long as Ms and Ms*and Ms* remain unchanged. remain unchanged.

ExampleExample; If k*y*(UK)/ky(USA) =1/2; and Ms(USA)/Ms*(UK)=4 then;; If k*y*(UK)/ky(USA) =1/2; and Ms(USA)/Ms*(UK)=4 then;

R = 4 (1/2) = 2, i.e., $ 2 = £ 1R = 4 (1/2) = 2, i.e., $ 2 = £ 1

Note:Note: Changes in R are positively Changes in R are positively proportionalproportional to changes in Ms and to changes in Ms and inversely proportionalinversely proportional

to changes in Ms*to changes in Ms*

If Ms increases by 10% in relation to Ms* If Ms increases by 10% in relation to Ms* R increases by 10% (depreciation) R increases by 10% (depreciation)

S=MS(US)/MS(UK) , as S increases R rises (a depreciation of the $)

The relationship between Ms in US relative to UK

depreciation

FIGURE 1 Relative Money Supplies and Exchange Rates.FIGURE 1 Relative Money Supplies and Exchange Rates.

Note the following:Note the following:

1.1. R is derived from the demand for nominal money balances that does R is derived from the demand for nominal money balances that does not include not include interest ratesinterest rates

2.2. Exchange rates adjusts to clear money markets in each country without Exchange rates adjusts to clear money markets in each country without any flow of reserves. Hence For a small open economy R depends on any flow of reserves. Hence For a small open economy R depends on PPP and LOOPPPP and LOOP

3.3. In a small open economy, the PPP determines the price level under In a small open economy, the PPP determines the price level under fixed exchange rates system and the exchange rates under flexible fixed exchange rates system and the exchange rates under flexible exchange rates system.exchange rates system.

IV. Expectations, Interest Differentials and Exchange RatesIV. Expectations, Interest Differentials and Exchange Rates

Exchange rates depend not only on relative growth of Ms and y, Exchange rates depend not only on relative growth of Ms and y, but also on inflation expectations and expected changes in but also on inflation expectations and expected changes in exchange rates.exchange rates.

An increase in the expected rate of inflation in a nation leads to an An increase in the expected rate of inflation in a nation leads to an immediate equal depreciation of the nation’s currency.immediate equal depreciation of the nation’s currency.

An expected change in the exchange rate will also lead to an An expected change in the exchange rate will also lead to an immediate change in the exchange rate.immediate change in the exchange rate.

Using the theory of uncovered interest arbitrageUsing the theory of uncovered interest arbitrage

i – i* = EAi – i* = EA

EA = expected appreciation of foreign currencyEA = expected appreciation of foreign currency

If i = 6% and i* = 5%, the If i = 6% and i* = 5%, the expectationexpectation is that the foreign is that the foreign currency appreciates by 1% in order to make returns on currency appreciates by 1% in order to make returns on investing at home and abroad equal as required by investing at home and abroad equal as required by uncovered interest parity.uncovered interest parity.

If the If the expected appreciationexpected appreciation of the foreign currency of the foreign currency increasesincreases this would lead to an immediate this would lead to an immediate capital outflowcapital outflow and expected and expected appreciation appreciation falls to go back to uncovered falls to go back to uncovered interest parity.interest parity.

If interest differentials changes, the new If interest differentials changes, the new expected expected appreciationappreciation will be different, but it will always have to will be different, but it will always have to equalequal the interest differentials so as to satisfy the the interest differentials so as to satisfy the uncovered interest parity.uncovered interest parity.

V. Asset Market Model and Exchange RatesV. Asset Market Model and Exchange Rates

The asset market or portfolio balance approach differs from the monetary The asset market or portfolio balance approach differs from the monetary approach in that:approach in that:

domestic and foreign bonds are assumed to be imperfect substitutesdomestic and foreign bonds are assumed to be imperfect substitutes , and , and postulates postulates

the exchange rate is determined in the process of the exchange rate is determined in the process of equilibrating or equilibrating or balancing the stock or total demand and supply of financial assetsbalancing the stock or total demand and supply of financial assets (of (of which money is one) in each country.which money is one) in each country.

Individuals and firms hold their financial assets in some combination of Individuals and firms hold their financial assets in some combination of domestic and foreign assets. The incentive to hold bonds results from the domestic and foreign assets. The incentive to hold bonds results from the yield or interest they provide. But they carry the risk of default, the risk yield or interest they provide. But they carry the risk of default, the risk arising from the variability of their market value over time. Domestic and arising from the variability of their market value over time. Domestic and foreign bonds are imperfect substitutes. Foreign bonds pose some additional foreign bonds are imperfect substitutes. Foreign bonds pose some additional risk with respect to domestic bonds. risk with respect to domestic bonds.

Holding domestic money, though riskless, but provides no interest. The Holding domestic money, though riskless, but provides no interest. The opportunity cost of holding domestic money is the yield forgone on holding opportunity cost of holding domestic money is the yield forgone on holding bonds. The higher the interest on bonds, the smaller is the quantity of bonds. The higher the interest on bonds, the smaller is the quantity of money they will want to hold.money they will want to hold.

The choice however is not only between holding domestic money and bond, but The choice however is not only between holding domestic money and bond, but also foreign bond. Foreign bond carries additional risk; the foreign currency also foreign bond. Foreign bond carries additional risk; the foreign currency may depreciate. However, holding a foreign bond allows individuals to spread may depreciate. However, holding a foreign bond allows individuals to spread their risk. their risk.

Factors that affect the portfolio choice are; tastes and preferences, wealth, the Factors that affect the portfolio choice are; tastes and preferences, wealth, the level of domestic and foreign interest rates, expectations about future levels of level of domestic and foreign interest rates, expectations about future levels of inflation rates at home and abroad ..etc. A change in the underlying factors will inflation rates at home and abroad ..etc. A change in the underlying factors will prompt holders to reshuffle their portfolio until they achieved the desired prompt holders to reshuffle their portfolio until they achieved the desired (equilibrium) portfolio.(equilibrium) portfolio.

An increase in interest rates raises the demand for the domestic bond, but An increase in interest rates raises the demand for the domestic bond, but reduces the demand for domestic money and the foreign bond. As investors will reduces the demand for domestic money and the foreign bond. As investors will sell the foreign bond, exchange foreign currency into domestic currency to sell the foreign bond, exchange foreign currency into domestic currency to acquire more of the domestic bond the exchange rate falls (appreciation).acquire more of the domestic bond the exchange rate falls (appreciation).

An increase in foreign interest rate raises the demand for the foreign bond but An increase in foreign interest rate raises the demand for the foreign bond but reduces the demand for the domestic bond and demand for money. The reduces the demand for the domestic bond and demand for money. The exchange rate rises (depreciation).exchange rate rises (depreciation).

In general, an increase in wealth increases the demand for money for domestic In general, an increase in wealth increases the demand for money for domestic and foreign bonds. In case the investors buy foreign currency to acquire more and foreign bonds. In case the investors buy foreign currency to acquire more of the foreign bond, the exchange rate also rises (depreciation). of the foreign bond, the exchange rate also rises (depreciation).

The asset market model is also called the The asset market model is also called the portfolio balance approachportfolio balance approach. If . If investors demand more of the foreign bond either because foreign interest rose investors demand more of the foreign bond either because foreign interest rose or their wealth increase, the demand for the foreign currency increases and this or their wealth increase, the demand for the foreign currency increases and this causes an increase in R (depreciation). causes an increase in R (depreciation).

If investors sell the foreign bond either because reduction of foreign interest, or If investors sell the foreign bond either because reduction of foreign interest, or a reduction of their wealth, the supply of foreign currency increases causing a a reduction of their wealth, the supply of foreign currency increases causing a decrease in R (appreciation) decrease in R (appreciation)

Hence Exchange rate is determined in the process of reaching Hence Exchange rate is determined in the process of reaching equilibrium in each financial market. equilibrium in each financial market.

VI. Extended Asset Market ModelVI. Extended Asset Market ModelVI.A Extended VariablesVI.A Extended Variables Extended asset market model adds more complex set of variables that Extended asset market model adds more complex set of variables that

determines the demand for money (M), the demand for the domestic bond (D) determines the demand for money (M), the demand for the domestic bond (D) and the foreign bond (F), which in the previous model depend on interest and the foreign bond (F), which in the previous model depend on interest differentials (i-i*). differentials (i-i*).

The variables added are the expected change in the spot rate (EA), the risk The variables added are the expected change in the spot rate (EA), the risk premium (RP), the level of real income (Y), the domestic price level (P), the premium (RP), the level of real income (Y), the domestic price level (P), the wealth of the nation (W).wealth of the nation (W).

We know that the uncovered interest parity condition is i-i* = EA, EA is We know that the uncovered interest parity condition is i-i* = EA, EA is included as an additional explanatory variable in the demand function for M, D, included as an additional explanatory variable in the demand function for M, D, and F in the assets market model. and F in the assets market model.

Since the domestic and foreign bond are imperfect substitutes, there is an extra Since the domestic and foreign bond are imperfect substitutes, there is an extra risk in holding the foreign bond arising from unexpected changes in the risk in holding the foreign bond arising from unexpected changes in the exchange rate (currency risk), and/or limitations foreign countries can put on exchange rate (currency risk), and/or limitations foreign countries can put on transferring earnings back home. The uncovered interest parity condition must transferring earnings back home. The uncovered interest parity condition must be extended to be:be extended to be:

i – i* = EA – RP i – i* = EA – RP So that So that

i = i* + EA – RPi = i* + EA – RP

This means that interest rate in the home country (i) must be equal to the This means that interest rate in the home country (i) must be equal to the interest rate in the foreign country (i*) plus the expected appreciation (EA) interest rate in the foreign country (i*) plus the expected appreciation (EA) minus the risk premium (RP) on holding foreign assets.minus the risk premium (RP) on holding foreign assets.

Example, if i = 4%, i* = 5% and EA = 1%, then RP on the foreign bond must Example, if i = 4%, i* = 5% and EA = 1%, then RP on the foreign bond must be 2% in order to be at uncovered interest parity. If RP is only 1%, residents be 2% in order to be at uncovered interest parity. If RP is only 1%, residents will buy more foreign bonds until the interest parity condition is satisfied. will buy more foreign bonds until the interest parity condition is satisfied.

The extended demand functions for M, D, and F are given by the following The extended demand functions for M, D, and F are given by the following equations: equations:

- - - + + + +- - - + + + +

M=f( i, i*, EA, RP, Y, P, W) M=f( i, i*, EA, RP, Y, P, W)

+ - - + - - ++ - - + - - +

D=f( i, i*, EA, RP, Y, P, W) D=f( i, i*, EA, RP, Y, P, W)

- + + - - - +- + + - - - +

F=f( i, i*, EA, RP, Y, P, W) F=f( i, i*, EA, RP, Y, P, W)

Expected signs (direction of the relationship) are above each variable. Expected signs (direction of the relationship) are above each variable.

At equilibrium between the demand for M, D and F and the supply of these At equilibrium between the demand for M, D and F and the supply of these assets, interest rates and exchange rates are simultaneously obtained. But since assets, interest rates and exchange rates are simultaneously obtained. But since M, D and F are substitutes, any change in the value of any of the variables of M, D and F are substitutes, any change in the value of any of the variables of the model will affect every other variable of the model. For example any switch the model will affect every other variable of the model. For example any switch to or from money balances and/or domestic bonds into foreign bonds affects the to or from money balances and/or domestic bonds into foreign bonds affects the exchange rate because they involve the exchange of currencies. exchange rate because they involve the exchange of currencies.

VI.B Portfolio Adjustments and Exchange RatesVI.B Portfolio Adjustments and Exchange Rates

EXAMPLE 1: suppose that the central bank engages in open market sale of government

securities (D) MS ↓ i ↑ M and F ↓, but D ↑. Foreign residents are also expected to demand more D inflow of funds. The sale of F and purchase of D involves the sale of foreign currency and purchase of domestic currency appreciation of the domestic currency (depreciation of the foreign).

EXAMPLE 2: Suppose that EA is more than is previously believed, M and D ↓ but F ↑ i

↓, capital outflow of funds. But the higher demand for foreign currency leads to appreciation of the foreign currency (depreciation of the domestic).

EXAMPLE 3: If Y and Y* ↑ ↑ M, but D and F ↓ (due to more demand for M),

appreciation of the domestic currency (depreciation of the foreign), these will affect other variables in the model until equilibrium is achieved.

VII. Exchange Rate DynamicsVII. Exchange Rate Dynamics

Exchange rate dynamics: Exchange rate dynamics: the change in the exchange rate over time as it the change in the exchange rate over time as it moves toward a new equilibrium level after an exogenous change. moves toward a new equilibrium level after an exogenous change.

A- Exchange rate overshooting (R. Dornbusch 1976) A- Exchange rate overshooting (R. Dornbusch 1976)

We know that changes in the set of variables mentioned above lead investors to We know that changes in the set of variables mentioned above lead investors to reallocate financial assets to balance their portfolio. Financial assets are reallocate financial assets to balance their portfolio. Financial assets are accumulated over a long period of time, i.e., they are accumulated over a long period of time, i.e., they are very largevery large in relation to in relation to the annual flows (changes in their stock) through savings and investments. the annual flows (changes in their stock) through savings and investments.

Changes in one of the variables (e.g., interest rates) affect returns and costs of Changes in one of the variables (e.g., interest rates) affect returns and costs of portfolios, and is likely to lead to a portfolios, and is likely to lead to a very rapid changevery rapid change in their stocks to in their stocks to reestablish portfolio balance. reestablish portfolio balance.

If all markets are in equilibrium, an increase in MS If all markets are in equilibrium, an increase in MS ↓ interest, ↓ interest, an an immediate (immediate (very largevery large) shift from domestic bonds to money and foreign bonds ) shift from domestic bonds to money and foreign bonds over a very short period of time. Now compare this with the over a very short period of time. Now compare this with the gradualgradual change in change in trade flows due to e.g., a depreciation, which takes place over a longer period trade flows due to e.g., a depreciation, which takes place over a longer period of time. Hence stock adjustments in financial assets are much larger and of time. Hence stock adjustments in financial assets are much larger and quicker than adjustments in trade flows.quicker than adjustments in trade flows.

The differences in the size and quickness of stock adjustments in financial The differences in the size and quickness of stock adjustments in financial assets as opposed to trade flow have very important implications for the process assets as opposed to trade flow have very important implications for the process by which exchange rates are determined and change (by which exchange rates are determined and change (dynamicsdynamics) over time.) over time.

For example if there is an unexpected increase in MS For example if there is an unexpected increase in MS ↓ interest, ↓ interest, large and large and quick increase in the demand for foreign currency quick increase in the demand for foreign currency an immediate and large an immediate and large depreciation of domestic currency which is likely to swamp the smaller and depreciation of domestic currency which is likely to swamp the smaller and gradual changes in exchange rate resulting from changes in real markets (e.g., gradual changes in exchange rate resulting from changes in real markets (e.g., trade flows). This explains why in the short run, exchange rates tend to trade flows). This explains why in the short run, exchange rates tend to overshootovershoot (bypass) their long run equilibrium levels as they move towards (bypass) their long run equilibrium levels as they move towards equilibrium. But over time as the cumulative contribution to adjustment coming equilibrium. But over time as the cumulative contribution to adjustment coming from the real sector (e.g., trade) reverses exchange rate movement and from the real sector (e.g., trade) reverses exchange rate movement and overshooting is eliminatedovershooting is eliminated..

Note that if the real sector responds immediately as financial sectors do, there Note that if the real sector responds immediately as financial sectors do, there would be no exchange rate overshooting.would be no exchange rate overshooting.

B- Time Path to a New equilibrium Exchange RateB- Time Path to a New equilibrium Exchange Rate

Explanation: look at figure 2, and note that i – i* = EA, i.e, Explanation: look at figure 2, and note that i – i* = EA, i.e,

i = i* + EA, if EA = 0, then uncovered interest parity condition is i = i*, before i = i* + EA, if EA = 0, then uncovered interest parity condition is i = i*, before the increase in MS. The rise in MS leads to a reduction in i. Since i < i*, we the increase in MS. The rise in MS leads to a reduction in i. Since i < i*, we expect the foreign currency to depreciate and the domestic currency to expect the foreign currency to depreciate and the domestic currency to appreciates, for uncovered interest parity to be satisfied again. appreciates, for uncovered interest parity to be satisfied again.

The only way we can expect the domestic currency to appreciate in the future The only way we can expect the domestic currency to appreciate in the future and still end up with a net depreciation of 10% (in the long run), is for the and still end up with a net depreciation of 10% (in the long run), is for the domestic currency to depreciate by more than 10%, and then gradually domestic currency to depreciate by more than 10%, and then gradually appreciate in the long run, in order to eliminate the overshooting. appreciate in the long run, in order to eliminate the overshooting.

FIGURE 2 Exchange Rate Overshooting: Permanent increase in US money supply.FIGURE 2 Exchange Rate Overshooting: Permanent increase in US money supply.

An increase in MS by 10% An immediate decline in interest

No immediate impact on prices

The dollar immediately depreciates

By more than 10% (excessive

Depreciation by 16%, overshooting)

Gradual appreciation

to eliminate overshooting

FIGURE 3 Overshooting of Dollar Exchange Rates.FIGURE 3 Overshooting of Dollar Exchange Rates.

Fixed exchange rates period

Wild fluctuations of the dollar rates are an indication of overshooting