Economics of International Finance Econ. 315

Economics of International FinanceEcon. 315 Chapter 4: Exchange Rate Determination

I. Purchasing Power Parity Theory (PPP) (1) The Law of One Price (LOOP) • the same good (x) in different competitive markets must sell for the same price in the absence of transportation costs and trade barriers between these markets i.e., Px= (R) . (P*x) (2) Absolute PPP: • Is the application of the law of one price across countries for all goods and services, or for representative groups (baskets) of goods and services: P = (R) . (P*)  R= P/P*

According to the equation, the equilibrium exchange rate between two currencies equals the ratio of the price levels in the two nations • 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. This is the LOOP. • According to LOOP (a given commodity should have the same price, so that the purchasing power of the two currencies is at parity). • 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 it in EMU area. This commodity arbitrage causes the price of wheat to be the same in the two markets (assuming no transportation costs or subsidies ..etc).

(3) Relative PPP theory • Change in the exchange rate should be proportional to the relative change in the price levels (inflation) in the two nations over the same period. R1 = ((p1/p0)/(p*1/p*0)).R0 • 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 of the EMU area, while in the US the price increases by 50%  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)]

Application: BIG MAC INDEXThe Economist'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 basket of goods and services around the world. Our basket is a burger: a McDonald’s Big Mac.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 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 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 Chinese yuan, at 56% below its PPP rate; several other Asian currencies also appear to be 40-50% undervalued.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-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. 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% overvalued. Hence European finance ministers’ beef with the low level of the yen. Source: The Economist.

Empirical tests of PPP • PPP works well for highly traded goods, e.g., wheat and steel, but less well for all traded goods together, and not so well for all goods (which includes non-traded commodities). • PPP works reasonably well over very long periods of time, and not well in the short run. • PPP works well in cases of purely monetary disturbances and in inflationary periods, but not so well in periods of monetary stability and not well in at all in situations of major structural change. Reasons why PPP may fail empirically: • Trade barriers, transportation costs, and non-tradable goods and services • Imperfect competition in product markets (price discrimination across markets) • Differences in price level measures (different “consumption baskets”)

Criticism • The prices of identical commodity baskets, when converted to a single currency, differ substantially across countries. • Relative PPP is more consistent with data, but it also performs quite poorly to predict exchange rates (it performs better over longer time spans for most countries –over 5-10 years). • PPP gives the R that equilibrates the trade in goods and services market, and completely disregarding the capital account. • PPP does not take non-traded goods and services into account. Their prices are not equalized by trade. • PPP does not take into account transportation costs or other obstructions to the free flow of international trade. But we care about PPP because it occupies a central position in the monetary asset market or portfolio balance approaches to BOP and exchange rate determination.

II. The monetary approach to BOP and exchange rates concentrates on monetary factors to predict long-run adjustment of nominal exchange rates: • Based on the PPP condition. • Uses the long-run assumption of fully flexible prices. • Price levels adjust to equate real aggregate money supply with real aggregate money demand: II.A Monetary approach to BOP under fixed exchange rates The demand for money: • Positively related to the level of nominal income • Stable in the long run. Md = kPY Md = the quantity of money demanded. 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 a given period. The average number of times each dollar is used to conduct transactions. P = price level (Price Index) Y = The real level of output (income)

The supply of money Ms = m (D+F) m = money multiplier (1/rrr) [we assume that it is constant] D = domestic component of the nation’s monetary base. It is the domestic credit created by the nation’s monetary authorities, or the domestic assets backing the nation’s money supply. F = international component of the monetary base (international reserves of the nation, e.g., in US $), D+F = the monetary base. • Starting from the equilibrium where Md = Ms (m (D+F)), Case One: • an increase in Md can be satisfied either by: - an increase in D or - inflow of F (BOP surplus). • If D does not increase, the extra demand will be satisfied by an increase in F. • Hence, a surplus in BOP results from an excess in the stock of money demanded that is not satisfied by an increase in D.

Case Two: • An increase in D, and Ms in the face of unchanged Md, F flows out the nation and leads to a fall in F (BOP deficit). • 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. Note That: • Under fixed exchange rate the nation has no control over its money supply system. The size of Ms will be the one that is consistent with BOP equilibrium. • The nation’s BOP surplus or deficit is temporary and self correcting in the long run. • After any excess demand or supply of money is eliminated through an inflow or outflow of funds, the BOP surplus or deficit is corrected and the 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 200 $ mn. to 220 $ mn. How??

II.B Monetary approach to BOP under flexible exchange rates. • Under flexible exchange rates, BOP is immediately corrected by automatic changes in exchange rates which causes prices to change without any flow of money or reserves. Here the nation retains control over its Ms and monetary policy: • A BOP deficit (resulting from excess Ms) leads to an automaticdepreciation causing the prices and Md to rise sufficiently to absorb the excess Ms and eliminate the BOP deficit without a change in F. 2. A BOP surplus (resulting from excess Md) leads to an appreciation causing the prices to fall and eliminate excess Md and BOP surplus without a change in F. • Under a flexible exchange rate system, a BOP disequilibrium is immediately corrected by an automatic change in exchange rates and without any international flow of money or reserves. • The actual exchange value of the currency is determined by the rate of growth of money supply and real income in the nation relative to other nations.

Note: • A currency depreciation results from excessive money growth in the nation over time. A currency appreciation results from inadequate money growth in the nation. • A nation facing greater inflationary pressures than other nations (resulting from more rapid growth in money in relation to real income and demand for money) will find its exchange rate rising (adepreciation). • A country facing lower inflationary pressures than the rest of the world, will find its exchange rate falling (an appreciation).

II.C Managed floating of exchange rate Under a managed floating , the authorities will intervene in foreign exchange markets and either lose or accumulate international reserves to prevent an excessive depreciation or appreciation of its currency, i.e., Under the system part of the BOP deficit is corrected by: 1. One Part by a depreciation of the domestic currency, 2. The other part is corrected by a loss of international reserves (F). 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 exchange rate system.

III. The monetary approach to exchange rate determination • If markets are competitive and there are no tariffs, transportation costs or other obstructions to trade, then according to LOOP the price of a commodity must be the same in two countries. P = R P* , then; R = P/P* • We can show that the exchange rate between two currencies is determined according to the monetary approach by using the money demand in the two nations. Md = k PY and Md*=k *P*Y* • In equilibrium Md = Ms and Md* = Ms* Ms*/Ms = k* P*Y*/k PY • Divide both sides by P*/P and Ms*/Ms , we get

P/P* = Msk*Y*/Ms*kY But since R=P/P* ; R = Ms k*Y* / Ms* kY • Since k*and Y* as well as k and Y are assumed constant R is constant as long as Ms and Ms* remain unchanged. Example; If k*y*(UK)/ky(USA) =1/2; and Ms(USA)/Ms*(UK)=4 then; R = 4 (1/2) = 2, i.e., $ 2 = £ 1 Note: • Changes in R are positively proportional to changes in Ms and inversely proportional to changes in Ms* • If Ms increases by 10% in relation to Ms*  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.

Note the following: • R is derived from the demand for nominal money balances that does not include interest rates • Exchange rates adjusts to clear money markets in each country without any flow of reserves. Hence For a small open economy R depends on PPP and LOOP • In a small open economy, the PPP determines the price level under fixed exchange rates system and the exchange rates under flexible exchange rates system.

IV. Expectations, Interest Differentials and Exchange Rates • Exchange rates depend not only on relative growth of Ms and y, but also on inflation expectations and expected changes in exchange rates. • An increase in the expected rate of inflation in a nation leads to an immediate equal depreciation of the nation’s currency. • An expected change in the exchange rate will also lead to an immediate change in the exchange rate. • Using the theory of uncovered interest arbitrage i – i* = EA EA = expected appreciation of foreign currency

If i = 6% and i* = 5%, the expectation is that the foreign currency appreciates by 1% in order to make returns on investing at home and abroad equal as required by uncovered interest parity. • If the expected appreciation of the foreign currency increases this would lead to an immediate capital outflow and expected appreciation falls to go back to uncovered interest parity. • If interest differentials changes, the new expected appreciation will be different, but it will always have to equal the interest differentials so as to satisfy the uncovered interest parity.

V. Asset Market Model and Exchange Rates • The asset market or portfolio balance approach differs from the monetary approach in that: • domestic and foreign bonds are assumed to be imperfect substitutes, and postulates • the exchange rate is determined in the process of equilibrating or balancing the stock or total demand and supply of financial assets (of which money is one) in each country. • Individuals and firms hold their financial assets in some combination of 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 arising from the variability of their market value over time. Domestic and foreign bonds are imperfect substitutes. Foreign bonds pose some additional risk with respect to domestic bonds. • Holding domestic money, though riskless, but provides no interest. The 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 money they will want to hold.

The choice however is not only between holding domestic money and bond, but also foreign bond. Foreign bond carries additional risk; the foreign currency may depreciate. However, holding a foreign bond allows individuals to spread their risk. • Factors that affect the portfolio choice are; tastes and preferences, wealth, the 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 prompt holders to reshuffle their portfolio until they achieved the desired (equilibrium) portfolio. • 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 sell the foreign bond, exchange foreign currency into domestic currency to 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 reduces the demand for the domestic bond and demand for money. The exchange rate rises (depreciation). • 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 of the foreign bond, the exchange rate also rises (depreciation). • The asset market model is also called the portfolio balance approach. If 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 causes an increase in R (depreciation). • 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 decrease in R (appreciation) • Hence Exchange rate is determined in the process of reaching equilibrium in each financial market.

VI. Extended Asset Market Model VI.A Extended Variables • Extended asset market model adds more complex set of variables that 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 differentials (i-i*). • 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 wealth of the nation (W). • 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, and F in the assets market model.

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 exchange rate (currency risk), and/or limitations foreign countries can put on transferring earnings back home. The uncovered interest parity condition must be extended to be: i – i* = EA – RP So that i = i* + EA – RP • 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) 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 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.

The extended demand functions for M, D, and F are given by the following equations: - - - + + + + M=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) • 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 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 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 exchange rate because they involve the exchange of currencies.

VI.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 Dynamics • Exchange rate dynamics: the change in the exchange rate over time as it moves toward a new equilibrium level after an exogenous change. A- Exchange rate overshooting (R. Dornbusch 1976) • We know that changes in the set of variables mentioned above lead investors to reallocate financial assets to balance their portfolio. Financial assets are accumulated over a long period of time, i.e., they are very large in relation to 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 portfolios, and is likely to lead to a very rapid change in their stocks to reestablish portfolio balance.

If all markets are in equilibrium, an increase in MS  ↓ interest,  an immediate (very large) shift from domestic bonds to money and foreign bonds over a very short period of time. Now compare this with the gradual change in 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 quicker than adjustments in trade flows. • 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 by which exchange rates are determined and change (dynamics) over time.

For example if there is an unexpected increase in MS  ↓ interest,  large and quick increase in the demand for foreign currency  an immediate and large 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., trade flows). This explains why in the short run, exchange rates tend to overshoot (bypass) their long run equilibrium levels as they move towards equilibrium. But over time as the cumulative contribution to adjustment coming from the real sector (e.g., trade) reverses exchange rate movement and overshooting is eliminated. • Note that if the real sector responds immediately as financial sectors do, there would be no exchange rate overshooting.

B- Time Path to a New equilibrium Exchange Rate • 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 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 appreciates, for uncovered interest parity to be satisfied again. • 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 domestic currency to depreciate by more than 10%, and then gradually appreciate in the long run, in order to eliminate the overshooting.

An increase in MS by 10% An immediate decline in interest Gradual appreciation to eliminate overshooting The dollar immediately depreciates By more than 10% (excessive Depreciation by 16%, overshooting) No immediate impact on prices FIGURE 2 Exchange Rate Overshooting: Permanent increase in US money supply.

Fixed exchange rates period Wild fluctuations of the dollar rates are an indication of overshooting FIGURE 3 Overshooting of Dollar Exchange Rates.

Economics of International Finance Econ. 315