Introduction to Exchange Rate Determination
Determination of the exchange rate in economics has been one of the major practices in economics that has attracted diverse views. Various theories have been developed to explain the determination of the exchange rate in various schools of thought. The monetary model has been one of the earliest models used in the of the exchange rate determination. However, it provides a good benchmark of comparing other models of interest determination. In addition, the model plays an imperative role in developing insights of capturing long trends. In the monetary model exchange rate are determined through the forces of demand and supply. Various essential parity relationships are also used in the determination of exchange such as the interest rate parity and the purchasing power parity (Obstfeld & Rogoff, 1996).
This paper seeks to compare the assumptions of the monetary model of exchange rate determination and the uncovered interest parity method of exchange determination. The monetary theory on exchange rate determination is based the interactions of demand and supply of the currency. The uncovered interest rate parity model is based on the notion that the interest differential between two countries will equal the expected exchange rate change. The uncovered interest rate parity model has continued to puzzle various economists due to its empirical failure. The model has been found to work only in the short run as investors borrow currency with low interest rate and invest in the currency with high interest (Sarno & Neely, 2002). The investor aims at taking advantage of the interest rate differential between the two currencies.
Monetary Model of Exchange Rate Determination
The determination of exchange rate has seen various developments in the last decades, with various economists developing various theories used in the determination of exchange rate. The developments have contributed significant theoretical and empirical explanations in the determination of the exchange rate. The monetary model of exchange rate determination is a flexible-price formulation. According to the monetary theory of exchange rate determination, exchange rate is the relative price of two currencies and their relative prices in relation to the demand and supply (Sarno & Neely, 2002).
In the monetary model the rate of exchange is determined by demand and supply of money. However, the supply of money is constant, since it’s determined by government through treasury and central bank. However, it does not imply that output in the economy is constant but implies that prices are perfectly flexible as shown in the diagram.
Price AS
Y* Y
The demand of money in the monetary model is based on the Cambridge quantity equation, which states that the real money balances are dependent on the real income. The equation below explains the Cambridge theory.
Md = kPy
The real money demand is dependent on the existing price. At equilibrium the supply of money is equal to the demand. The real interest rate in the monetary model is exogenous in the long run since it’s determined by the global markets due to the assumption of perfect capital mobility. The diagrammatical representation of the exchange rate determination under the monetary model is illustrated in the diagram shown.
Price AS
po
AD (Mo)
yo y
The intersection of aggregate demand and supply is the determinant of the domestic levels of price. However, the external equilibrium is obtained through incorporation of the purchasing power parity of the consumers. The diagrams below illustrate the determination of the external equilibrium in the monetary model.
Price p = ep0
P1
P0 AD (M1)
AD (M0)
eo e1 y0 y1
The equilibrium in the external market is obtained through the use of purchasing power parity relationships. In the process of incorporating the purchasing power parity, the floating exchange rate regime is considered. The absolute purchasing power parity is another major building block of the monetary model. The purchasing power parity states that, goods market arbitrage will have a tendency to move the exchange rate, to equate the prices in both countries involved in the exchange.
An decrease in money supply under a floating exchange regime leads to the appreciation of the domestic currency. This will lead to an increase in the price of exports, which might result to surplus in the balance of payment. However, the increase in price of domestic goods may make them to be less competitive in the international market. This might lead to a deficit in the current account as the local goods become less competitive in the global market. Under floating rate regime an contraction of the supply of money in the economy might lead to an increase in financial investments in a country.
Monetary Model Assumptions
The model assumes a flexible-price formulation, which requires numerous assumptions. First the model assumes an open economy where the country is assumed to engage in the international trade. The open market is based on various aggregate market, which include the labor market, goods market, money market, foreign exchange market domestic and foreign bonds market. However, the monetary model only considers one of the markets when determining the equilibrium. For example, the model may consider the money market (Krugman & Obstfeld, 2008).
The monetary model also assumes perfect substitutability of both the domestic and foreign assets. For example, the model assumes that both the domestic and foreign markets are merged to a single market. This has the effects of reducing the market considered in the monetary model in determining the rate of exchange. According to the monetary model of exchange rate determination, the rate of exchange adjusts freely to equate both demand and supply (Sarno & Neely, 2002).
For the flexible- pricing formulation to apply, it assumes that prices and wages are flexible to ensure the equilibrium of both goods and labor markets. The monetary model is a market clearing model based on the flexible-pricing model, where purchasing power parity in the national price levels is assumed to be continuous (Copeland, 2008).
Uncovered Interest Parity Model of Exchange Rate Determination
This model is based on the assumption that an investor is able to arbitrage in between two markets due to the existence of interest differential between two currencies. However, there have been difficulties by economists in determining the empirical viability of the uncovered interest model. The uncovered interest parity postulates that there exist interest differential between two countries, which should be equal to the exchange rate change expected. Various economists have conducted various investigations regarding the long run relationship between the rates of exchange and the term structure of the interest rates. The effect of short term interest real interest in the long run is opposite to what the standard exchange rate model postulates. However, when the differential of the real interest rate is controlled the domestic short term interest rate raises relative to the foreign short term interest rate while long term interest differentials remain unchanged. In such a case, the domestic currency tends to depreciate in the long run (Obstfeld & Rogoff, 1996).
The uncovered interest rate model in determining the rate of exchange also identifies as the period differential as a major factor determining the rate of exchange. For example, let’s consider two countries considered in our previous example i.e. US and UK. Let us assume that i is the first period interest rate in US and i* is the interest rate in the period the in UK. The considered period can be any time frame. The appropriate interest is that used in the domestic assets in a country over a certain period of time.
An investor who invests $10 in the US obtains $(1 + i) after the first period, under the domestic strategy. Under the foreign strategy the investor will expect to obtain $(1⁄e). If the money supply in the economy decreases at the current interest there will be a deficit in the supply of money given the interest rate. This requires the interest rate to rise, which leads to an increase in the returns on domestic deposits. To achieve an equilibrium in the exchange rate requires an appreciation of the domestic currency.
An equilibrium in the foreign exchange market is achieved when the interest rate on deposits in both economies offer similar expected rates on return. Such that
(1 + r$) e£/$⁄e£/$ = 1 + r£
In the uncovered interest parity model the domestic rate of interest must be similar to the foreign interest rate adding the expected rate of depreciation or appreciation of the domestic currency. If the interest rate of the pound relative to the dollar it will lead to depreciation of pound. The diagram below explains the relationship between the interest rate and the expected return of the pound relative to the dollar.
Exchange rate (e)
Expected £ return on $
The rates of exchanges adjust to facilitate maintenance of the interest parity. The digram below explains the adjustments of the interest rates, which facilitates maintenance of the interest parity.
Exchange rate (e) Return on pound deposits
Expected £ return on $
Rates of return (£)
In the short run, the prices are fixed given the output. The rate of interest determination is through the monetary market at the point where money demand is equal to the supply oif money. A decrease in money supply leads to an increase in the interest rate, since the level of income is given. The diagram below illustrates the decrese in money supply on the rate of interest.
Interest rate (r) Ms1 Ms0
r1
r0
L (y,r)
A decrease in money supply as shown in the diagram from Ms0 to Ms1 leads to an increase in the rate of interest from r0 to r1. The increase in the rate of interest leads to increased returns on domestic deposits. To ensure equilibrium in the foreign exchange the domestic currency has to appreciate, as shown in the diagram
exchange rate e$/£ Returns on dollar deposits
1
e2$/£ 2
e1$/£
return on $
this shows that the dollar has appreciated as the interest rate on the dollar has increased the returns on the dollar. To achieve an equilibrium in the foreign exchange market, the dollar has to appreciate against the pound as shown in nthe diagram.
Assumption of the Uncovered Interest Parity Model
The model assumes that the returns involved in the arbitrage are risk free and the opportunity of arbitrage exists due to the existence of interest differentials. The uncovered interest parity is assumed to the only determinant of the value of the forward exchange rate. Various studies have shown that the uncovered interest parity has been used by various banks in the determination of the value of an exchange rate. The model further assumes that the forward market only exists between major currencies (Krugman & Obstfeld, 2008).
The model also assumes that there exist interest differentials between two countries, which present an opportunity for an investor to arbitrage. For example, when the interest rates in the US are 5%, and interest rate in Japan is 17%, and the dollar is expected to appreciate by 14%, the investor will prefer investing in the dollar rather than yen. This raises the demand for the dollar, as more investors who were previously holding the Japanese Yen shift their currency to US dollar. However, the in the consequent periods, the demand of the Japanese yen may increase as the Japanese investors who had invested in the dollar move their money back to Japan (Weerapana, 2010).
References
Copeland, L. (2008). Exchange Rates and International Finance. New Jersey : Prentice Hall / Financial Times.
Krugman, P., & Obstfeld, M. (2008). Study Guide for International Economics: Theory and Policy. New york: Addison Wesley.
Obstfeld, M., & Rogoff, K. (1996). Foundations of International Macroeconomic. Massachusetts: MIT press.
Sarno, L., & Neely, C. (2002). How Well do Monetary Fundamentals Forecast Exchange rates? Federal Reserve Bank, 51 - 76.
Weerapana, A. (2010). Interest Rate Parity . Retrieved January 4, 2013, from https://docs.google.com/viewer?a=v&q=cache:1wiuN6L2GVsJ:www.wellesley.edu/Economics/weerapana/econ213/econ213pdf
