# What you will learn: UNIT 3. Traditional Flow Model. Determinants of the Exchange Rate

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1 What you will learn: UNIT 3 Determinants of the Exchange Rate (1) Theories of how inflation, economic growth and interest rates affect the exchange rate (2) How trade patterns affect the exchange rate (3) How the monetary sector of the economy affects the exchange rate (4) How investment demands/supplies affect the exchange rate (5) How Central bank activity affects the exchange rate (6) How interest rates reflect future exchange rate values and how to infer the market's forecast of the future exchange rate Definition: The exchange rate is the price of one currency in terms of another Most of the industrial world uses a floating exchange rate system. Under this system, market forces are the primary determinant of the exchange rate. The exchange rate is (for the most part) allowed to vary from day to day. There are a number of economic models which attempt to explain the movement of exchange rates through time. These include (but are not limited to) : the Traditional Flow Model, a Money Sector Model and the Asset Model Each of these models examines only one aspect of economic factors which might affect the exchange rate. For each of these models we will examine how: (1) price levels (P) (2) real income (Y) (3) and interest rates (i) affect the exchange rate (e) Traditional Flow Model (concentrates on the trade accounts ) Assumptions of the Traditional Flow Model (1) Traded goods and services are the ultimate link to the exchange rate. Economic factor Imports or exports exchange rate (2) No capital flows between countries. Like any other "good" the foreign exchange price is determined by the relative supply and demand for each currency. If we are talking about the \$/ exchange rate, this comes from the demand and supply of relative to the demand and supply of \$. Where does the demand for come from? Ans: From the US demand for European goods and services. 1

2 Derivation of the Demand for Assume a two good world where the French produce Good X and export this good to the US. price of good X in Exchange Rate \$/ Price of X in \$ U.S. Demand for X U.S. demand for (1) Given (2) Given (3)=(1)x(2) (4)=Given (5) = (1)x(4) Underlying the Demand Curve Responses of Demand for French Prices Rising Faster than US Prices US taste for French goods US real income (Y) US prices (P us ) vs. French Prices (P f ) US interest rates As French goods prices increase, French goods become relatively more expensive. Consequently, US citizens buy U.S. goods instead of the French goods (import substitution). With a decreased demand for French goods, there is a decreased demand for. US Real Income Growing Faster than French Real Income US Interest Rate Increases As real income increases in the US, US consumers demand more of all goods - including imports - for consumption (recall consumption varies directly with real income ). The US consumers must first buy before they buy French goods. Therefore the demand for increases. If the interest rate in the US increases, US citizens will save more. If they are saving they are consuming less of all goods, including imports. With a decrease in import demand, there is a decrease in the demand for. 2

3 Summary of Factors Affecting US Demand for Derivation of the Supply of Inflation Rate US > French Demand for US < French Demand for Interest Rate US interest rate Demand for US interest rate Demand for Assume a two good world where the US produces Good Z and exports this good to France. Real Income Growth Rate US Income Growth Rate US Income Growth Rate Demand for Demand for \$ Price of Good Z Exchange Rate \$/ Price of Good Z French Demand for Z French Supply of =Given =Given (2) (1) (2) (3)=(1) / (4)= Given (5)=(3)*(4) Underlying the Supply Curve French taste for US goods French real income (Y) French Prices (P f ) vs.us prices (P us ) French interest rates Responses of Supply of French Real Income Growing Faster than US Real Income French Prices Rising Faster than US Prices As French goods prices increase, French goods become relatively more expensive. Consequently, French citizens buy US goods instead of the French goods. In order for the French to buy US goods, they must first give up their for \$. As real income increases in France, French consumers demand more of all goods - including imports - for consumption (recall consumption varies directly with real income ). French consumers must first buy \$ before they buy US goods. Therefore the supply for increases. 3

4 French Interest Rate Increases Summary of Factors Affecting the French Supply of Inflation Rate US > French Supply of US < French Supply of Interest Rate French interest rate Supply of Real Income Growth Rate French interest rate French Income Growth Rate French Income Growth Rate Supply of Supply of Supply of If the interest rate in France increases, French citizens will save more. If they are saving more they are consuming less of all goods, including imports. With a decrease in import demand, there is a decrease in the demand for \$, so the supply of decreases. Market Equilibrium The equilibrium exchange rate is determined by the interaction of the supply and demand for foreign exchange. Combining the two graphs, the equilibrium exchange rate is given at point e0. Why can't e1 or e2 be the equilibrium exchange rate? What market forces lead to e0 being the market equilibrium? Ans:At e1 the quantity supplied would be greater than the quantity demanded, i.e. there would be a surplus at this rate. In competitive markets, the exchange rate would fall until it reached e0. At e2, quantity supplied would be less than the quantity demanded, i.e. there would be a shortage. In a competitive market, the exchange rate would be bid up until it reached e0. Predictions from the Traditional Flow Model Assume the market starts in equilibrium with S0, D0 and e0. What would happen to the \$/ rate under the following circumstance?: (1) US real income rises faster than in France (2) US Interest Rates Rise With higher real income in the US, US citizens buy more of all goods including imports. In order to buy more imports, they must first buy. The Demand for increases. This causes a temporary shortage of. The new equilibrium is at e1. Therefore, the \$ gets weaker. If the interest rate in the US increases, US citizens will save more. If they are saving they are consuming less of all goods, including imports. With a decrease in import demand, there is a decrease in the demand for. This will cause a temporary surplus of. The exchange rate will fall to the new equilibrium at e1. The \$ gets stronger. 4

5 (3) French real income rises faster than US real income (4) US prices rise faster than French Prices As real income increases in France, French consumers demand more of all goods - including imports French consumers must first buy \$ before they buy US goods. Therefore the supply for increases. This creates a temporary surplus and the exchange rate adjusts to e1. The \$ gets stronger. As the price of US goods increases, French citizens find US goods relatively more expensive. They buy fewer US goods, so they have to buy fewer US \$. The supply of decreases. US citizens also find the price of US goods to be relatively more expensive. US citizens therefore buy more French goods. In order to buy French goods they must first buy. The demand for therefore increases. The combined effect is a new equilibrium at e1. The \$ gets weaker. Money Sector Model (concentrates of relative prices (inflation rates) Ultimately based on Purchasing Power Parity (PPP) Economic factor inflation changes PPP exchange rate Combines, PPP, the Quantity theory and the Fisher Effect Assumes the expected real rate of interest is the same everywhere Purchasing Power Parity (PPP) PPP states that the same currency denomination price of the same good will be the same everywhere. Let s say we have 1 oz. gold trading in New York and London In NY the price is \$800 / oz In London the price is 440 /oz Exchange rate is 1.81 \$/ The \$ price in NY is simply \$800 / oz The \$ price in London is (440 )x(1.81 \$/ ) =\$ So the common currency price of gold is cheaper in London than in NY Traders would buy gold in London and sell it in NY but to buy gold in London, traders would first have to buy. The pound price would increase until the \$ denomination price of the gold was the same in both NY and London. PPP will hold because of the Law of One Price Two forces make Law of One Price hold (1) Final goods arbitrage - prices can deviate by the transaction (including taxes) or transportation costs (2) Input price equalization - if factors of production are free to move, then eventually, final goods prices will equalize. Value additivity says that in competitive markets, the final price of a good will be equal to the sum of the prices of the inputs used to make the goods. 5

6 Derivation of PPP P us = US price in \$ of the good P f = Foreign price of good in foreign currency e 0 = exchange rate stated as \$/ In equilibrium US price in \$ of the good = Foreign price in \$ of good P us = e 0 P f There are two versions of PPP P us = e 0 P f Absolute PPP % e 0 = % P us - % P f Relative PPP % Change in the exchange rate = US inflation Rate - Foreign Inflation Rate Note if % e 0 is positive, then the \$ is depreciating Defining the Quantity Theory Quantity Theory of Money M V = P Y M = Nominal Money Supply V = velocity of Money P = price level Y = real income / output velocity of money = number of times a dollar changes hands over a given period of time. Over time one would think velocity would be getting bigger. Why? The quantity theory can also be written % M + % V = % P + % Y Assume % V is zero because the other variables change so much faster. Then we get % M = % P + % Y Notation: E( ) is read expected So if % P denotes inflation, then E(% P ) denotes expected inflation 6

7 Quantity Theory of Money with % V=0 The Fisher Equation E(% P) = E(% M) E(% Y) i = E(R) + E (% P ) Fisher Equation The expected inflation rate is equal to the expected growth rate in nominal money supply, minus the expected growth in real income Inflation is caused when the nominal money supply grows more than the real GNP growth rate. The nominal interest rate, i, is equal to the sum of the expected real rate of return, E(R) and the expected inflation rate, E (% P ) Combine PPP, the Quantity Theory and the Fisher Equation to make predictions about the exchange rate. 1) Ε(% e) = E(% Pus )- E(% Pf ) PPP 2a) E(% P US ) = E(% M US ) E(% Y US ) Quantity Theory 2b) E(% P f ) = E(% M f ) E(% Y f ) Quantity Theory 3a) i US = E(R US ) + E ( % P US ) Fisher Equation 3b) i f = E(R f ) + E ( % P f ) Fisher Equation Predictions for the Money Sector Model Prices rise in the foreign country faster than the US From Equation 1 1) Ε(% e) = E(% Pus ) - E(% Pf ) PPP E(% % e) ---> \$ stronger Real income in the US rises faster than in the foreign country From Equation 2a and 1 2a) E(% P US ) = E(% M US ) E(% Y US ) Quantity Theory 1) Ε(% e) = E(% Pus ) - E(% Pf ) PPP E(% Y US ) --->> E(% P US ) (by Quantity Theory ) --->>E( % e) (by PPP) --->> \$ stronger US Nominal interest rates higher than foreign interest rates i us > i f From equations 3a,3b and 1 and our assumption about expected real interest rates 3a) i US = E(R US ) + E ( % P US ) Fisher Equation 3b) i f = E(R f ) + E ( % P f ) Fisher Equation 1) Ε(% e) = E(% Pus ) - E(% Pf ) PPP --->> E(% % e ) ( by PPP ) -->> \$ weaker 7

8 US nominal money supply increase From Equation 2a and 1 2a) E(% P US ) = E(% M US ) E(% Y US ) Quantity Theory 1) Ε(% e) = E(% Pus ) - E(% Pf ) PPP E(% Mus) --->> E(% Pus) ( by Quantity Theory ) --->> E(% e ) ( by PPP) --->>\$ weaker Asset Model of Exchange Rate Determination Based on expected real after-tax risk adjusted interest rates People move their wealth to countries where they believe they can get the highest real after tax risk adjusted rate of return. In order to invest in a country you must first buy their currency. When a country has a higher real risk adjusted interest rate, their currency gets stronger. Factors which can make a countries real interest rates higher (1) Higher growth rate in real income - this increases the demand for funds and drives up the real rates (2) Government budget deficits that are not expected to be monetized. (3) Tight monetary policy. Intuition behind Asset Model Anything that you can envision that would make a country a better place to invest will attract capital to that country. As the capital flows in, that country s currency will tend to strengthen Central Bank Intervention Central banks attempt to manipulate the value of their country's currency by creating excess supply of their currency (to weaken it ) or excess demand for their currency (to strengthen it ). To strengthen the from e0 to e1 requires that the European Central bank purchase (Q1 - Q0) 's using some of its dollar holdings. Eventually the domestic supply of will decline and the domestic supply of \$ will increase. 8

9 Sterilized vs. Unsterilized Intervention In the preceding example, the intervention in the foreign exchange market may have undesired effects on the respective domestic economies. US inflation will tend to rise and European inflation will tend to fall. In this example, the intervention was unsterilized because no action was taken by the banks to protect the domestic economy from the impact of the intervention. The central banks can protect the domestic economy from the impact of the intervention using sterilized intervention. Sterilized intervention is when the central banks use open market operations to counteract the effect of a currency intervention. In the above example, the European Central bank would purchase European Treasury bonds ( thereby increasing the European money supply ) and the US Fed. would sell US Treasury bonds (thereby decreasing the US money supply). The world is now holding more US debt and less European debt. If the two types of debt are viewed as perfect substitutes, then nothing will happen to exchange rates or interest rates once the sterilization takes place. Uncovered Interest Parity (UIP) E (% e ) = i US - i f Derivation of UIP (UIP) 1. E( Rus) = E(Rf)Assume the expected real rate of interest is the same across all countries. 2. ius - E(% Pus) = if - E(% PF) Fisher E ect: 3. E(% Pus) - E(% PF)= ius - if Rearrange E(% e ) = ius - if Use definition of PPP Rearranging UIP Implications of UIP i US = i f + E (% e ) E (% e ) = i US - i f The US interest rate (in \$) is equal to the foreign interest rate (on ) plus an expected adjustment of the exchange rate The net effect is that if UIP holds, the dollar return (or cost) is expected to be the same in both countries. Implications of UIP cont. You can think of it as If I gain on the interest rate, I should expect to lose on the exchange rate If i US =4% and i f =6%, if you decide to invest in the foreign country to gain 2% on the interest rate, then you should expect to bring back that are 2% weaker so that the net return in dollars is 4%, the same as you would have gotten if you had invested directly in the US. Implications of UIP cont. The big picture is that if (1) capital is free to flow and (2) the assets in the two country are in the same risk class UIP is more likely to hold It won t matter where you borrow or invest To get a better return (or cost) from investing (borrowing) overseas, (1) there must be some capital restriction or (2) the risk is not the same Market Forecast of the Exchange Rate Change If we combine the approximation from CIP D= i US - i f With UIP E(% e ) = i US - i f we get D = E(% e ) 9

10 The current observable forward rate is an unbiased forecast of the future spot rate if CIP and UIP hold For our purposes, this means that if you used the forward rate as your forecast of the future spot rate, then your average error would be zero Caution: don t interpret this to mean that the errors would be small. They could be quite large, it s just that they would average to zero over time. 10

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