# The Exchange Rate In An Open Economy Economics Essay

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## Introduction

This paper deals with the determinants and dynamics of the exchange rate in an open economy with free movement of domestic and foreign capital. We review in detail the main monetary and portfolio models. Section 2 describes the exchange rates and interest rates used in both equilibrium models of flows as the equilibrium models in stock. Finally, Section 3 discusses the macroeconomics of exchange rate determination, incorporating expectations and emphasizing the recent approach of asset market. The flow equilibrium approach for the monetary model of balance of payments and the well-known Mundell-Fleming model which extends the IS-LM model with the addition of capital movements in the exchange rate determination.

According to the flow equilibrium approach, the exchange rate is determined as the

price of any good, that is, by supply and demand for currency, the same as

depend, in turn, flows of goods, services and external capital. This reflects mainly the period covering the decades of 50 and 60, characterized by low capital movements. Accordingly, in this approach exchange rate movements are explained by the behavior of the trade balance, ie the evolution of exports and imports of goods and services.

The asset market approach is more recent and developed in the decades of

70 and 80 years, a period characterized by a high exchange rate volatility in the short term that the former approach was unable to explain. Instead of the balance of flows of trade balance emphasizes the stock equilibrium condition of the capital account. As is known the 15 August 1971 formally collapses Bretton Woods system with the elimination of the dollar's convertibility into gold ordered by U.S. President Richard Nixon. In the years that follow, then, is implanted in the world a system of generalized floating of major currencies along with increased mobility and integration of international capital.

In the asset market approach, there are two types of models, monetary models with their versions of flexible and rigid prices, and portfolio balance models. Monetary models with flexible prices can be: no

expectations for perfect schemes floating exchange rate and floating

controlled, and both adaptive and rational expectations. Monetary models with sticky prices are all rational expectations. Among the main ones are the Dornbusch model that incorporates an equation of the Phillips curve, and variations of this model: first with trend inflation and real interest rate as a determinant of investment, and second with an aggregate supply function dependent on the real exchange rate. All these models treat the dynamics of the exchange rate and external shocks.

If the Mundell-Fleming model with fixed prices, it incorporates the uncovered interest parity under rational expectations (perfect prediction), the solution for the exchange rate is unstable. The instability is removed if we introduce an additional equation, assuming a slow adjustment of aggregate demand product. The result is a model of exchange rate overshooting, similar to Dornbusch model with sticky prices.

Finally, we study the portfolio model of exchange rate determination,

developed based on the work of Branson and Kouri. This model eliminates the

arbitrage equation, since, unlike previous ones, is not perfect substitutability between domestic assets and foreign assets. In addition, it incorporates a concept of external balance than the one used in the Mundell-Fleming model and its variants. The external balance is not the balance of payments, but the current account.

FUNDAMENTAL CONCEPTS AND IDENTITIES

2.1 Type of Nominal and Real Change The nominal exchange rate and real exchange rate are two relative prices associated with open economies with different currencies. The nominal exchange rate is the relative price of one currency against another.

## Parity Conditions

Is defined as the number of units of domestic currency per unit of foreign currency or, alternatively, as the price of one unit of foreign currency in domestic currency terms. When the price falls is said to have produced an appreciation of domestic currency. By contrast, if increases, there has been a depreciation or devaluation of domestic currency.

A decrease (increase) the nominal exchange rate is equivalent then to a

appreciation (depreciation) of the domestic currency.

The real exchange rate is the price of foreign goods in terms of assets

household. If the price of foreign goods is P * and domestic goods is P, the real exchange rate is equal to: e = EP * / P, where E is the nominal exchange rate. The real appreciation is a decrease in real exchange rate means that prices of domestic goods are relatively more expensive or that the prices of foreign goods in terms of domestic goods, have declined. The real depreciation is an increase in real exchange rate means that prices of foreign goods are relatively more expensive.

2.2 Interest Parity in an economy with open financial markets investors should decide on the distribution of financial wealth in domestic and foreign assets. This decision largely depends on the expected returns of both assets, the investment risk and foreign exchange gain, as the domestic and international assets are not listed in the same currency. The relationships between these variables are represented by the following rates:

a) The cover of the interest parity (Covered Interest Parity - CIP). It is assumed that

domestic and international assets have similar characteristics, but pay

different interest rates: r and r * respectively. In addition, assets are listed in different currencies, so the external asset returns are affected by a gain (or loss). If an investor wants to invest in country's foreign asset must first convert their money into dollars, at a certain rate, and then acquire the asset. But, at the time that ends your investment and get the interest, be the reverse, converting their dollars into soles. If this operation the exchange rate is less than the force at the time of the first transaction, the investor will have lost capital as a result of exchange rate fluctuations. If the investor wants to "cover" of foreign exchange risk would have to hire in the futures market, forward exchange rate, ie the exchange rate that prevails at the time believed that the investment is paid. If

the effective exchange rate is less than the forward rate, the investor will have earned an award term, but if over-term capital will be lost. To express the relationship of parity in formal terms, suppose that the asset has a return home (1 r) per dollar, while while the return on assets abroad is: (EF / E) (1 r *), where E is the spot exchange rate and EF is the forward rate. If the international arbitration gets to equalize internal and external returns.

This relationship indicates that the domestic interest rate must be equal to the interest rate

international, plus the prize (or discount) term obtained by the exchange difference.

b) The uncovered interest parity (Uncovered Interest Parity - UIP). If

investors do not "cover" the risk in the futures market, taking into account fluctuations in the exchange rate through the expected exchange rate (Ee), ie, their expectations about the future value of the exchange rate.

2.3 Purchasing Power Parity (purchasing power parity - PPP)

This concept was developed in 1914-1918 by Gustav Cassel. Power parity

Cart (PPP) is not nothing but a reformulation of the "law of one price", whereby a homogeneous product must have the same price worldwide. If P is the domestic price quoted in local currency and P * is the foreign price for the same well, but quoted in foreign currency, then the PPP, states:

P = EP *

The PPP is true if and only if there are no information costs, transportation costs and

other international trade restrictions (tariffs, quotas, etc..). Obviously, this is

a course very restrictive. Less restrictive version, or relative of PPP states that:

where s is an index that measures the deviation of absolute parity. If PPP is fulfilled, as absolute, s is equal to one.

2.4 Parity of real interest rates

Are met simultaneously purchasing power parity and uncovered interest parity, then the domestic real interest rates and external must be equal. To demonstrate this we start from the definition of real interest rates:

From these two equations we obtain:

If we express the ratio of the PPP in terms of expected rates of change in their respective variables, then:

Consequently, if satisfied parity uncovered interest rates and purchasing power parity, the difference between real interest rates will be equal to zero, then:

R R r = r *

This equality between the domestic real interest rate and real interest rates internationally, is known as Fisher open condition. It was Irving Fisher (1965) which defined the real interest rate as the current rate minus the expected inflation rate.

2.5 Expectations and Interest Parity does not cover

In most of the models analyzed here, your supposed to meet the uncovered interest parity:

This relationship takes different versions, depending on the type of expectations formation.

If the expected exchange rate is assumed given or constant, ie, E e, then the arbitrage relationship becomes:

1 r r * E Ee - =

(1)

This equation indicates a negative relationship between exchange rate and domestic interest rates. But it also indicates that an increase in international interest rates has a positive effect on the exchange rate. Finally, an upward revision of expectations, increases the exchange rate for given interest rates. With static expectations, ie, assuming that the expected exchange rate equals the current exchange rate, the equation of the uncovered interest parity is reduced to:

r = r *

Finally, if you enter the event perfect prediction under the hypothesis of rational expectations, the uncovered interest parity incorporates the actual change in the exchange rate (& e). Ie

r = r * e &

MACROECONOMICS OF DETERMINATION AND EXCHANGE RATE DYNAMICS

There are two main approaches to explain how to determine the exchange rate in an economy. The traditional approach flow, as its name implies, emphasizes the role of international flows of goods in determining the exchange rate. A more recent approach, called asset market approach, believes that the exchange rate is determined by the equilibrium conditions of the existing stocks of financial assets.

## BALANCE OF PAYMENTS AND THE ASSET MARKET

The models of the first approach corresponds to a period of low capital mobility. The opposite occurs with the second approach models. The first, are unable, therefore, to explain the volatility of the exchange rate, a phenomenon that characterizes the period of the 70's to today.

## Forward

## Premium

## Interest

## Differential

## Inflation

## Differential

## Rate of change

## of spot rate

Fisher Open Relationship

Unbiased Expectations Hypothesis

Interest Rate Parity

Purchasing Power Parity

3.1 The flow balance approach: Mundell - Fleming Mundell-Fleming model developed in the early 60's through the work of Robert Mundell and Marcus Fleming4. Its main purpose was to show how monetary and fiscal policies can be used for the simultaneous achievement of internal and external objectives in an economy that is supposed to be small and open. Its main feature is that it extends the IS-LM model by incorporating the movements of capital in determining the exchange rate. The assumption of small open economy implies that the policies pursued by the government do not affect macroeconomic aggregates around the world. It is considered that the prices and incomes around the world are given.

## FORECASTING

When the exchange rate is flexible, the monetary authority loses control over the exchange rate but regains control of the money supply. In formal terms, the exchange rate becomes an endogenous variable. Being flexible, the exchange rate is adjusted to correct the imbalances in the external sector, therefore, the balance of payments will always be in balance (& R = 0) with which the distinction between short and long term disappears.

If we ignore for the moment the effect of expected changes in the exchange rate under the assumption of static expectations, the standard version of the Mundell - Fleming is summarized in the following equations:

0 (, *) (,,) (*) (,,) () () (, *) (,,) Gm K EY EM XEY rr L r and b RD

EY EM YCYGI XEY Gm r ddd = - - = = -

(4)

Totally differentiating these equations and ordering in terms of excess demand, we obtain:

(2)

(3)

under the assumption that the condition of Marshall-Lerner Comparative Statics with Imperfect Capital Mobility Expansionary Fiscal Policy matrix multipliers allows us to observe that the only ambiguous effect on the exchange rate is the rising tax burden. An increase in aggregate demand shifts the curve to the right (IS '). Graph shows two panels:

(5)

low capital mobility in the upper panel (BP curve slope greater than the slope of the LM) and high mobility in the bottom panel (BP curve slope less than the slope of the LM).

In the top panel (with low capital mobility) the new internal equilibrium (point B) is located below the BP curve, ie no internal equilibrium with the external deficit.

As the exchange rate is flexible, it must be adjusted to improve the balance of payments. Indeed, the domestic currency depreciates. Given the Marshall - Lerner condition, the effect of devaluation on aggregate demand is expanding: the IS curve will move again but this time to IS.'' The devaluation will also have the effect of improving the competitiveness of the economy. Consequently, the BP curve will move to the right (BP '). In the final equilibrium (point C) the effects of fiscal expansion would be an increase in real output and interest rate and currency depreciation.

In the bottom pane, point B is on the BP curve in the area of surplus. Type

change must fall to correct this imbalance. With the revaluation of the currency will have two effects: a recession in the real sector that makes the IS curve moves to IS''and a deterioration in external competitiveness caused by the appreciation curve that moves BP to BP. " The final balance model (C) shows a rise in output and interest rates, and an appreciation of domestic currency.

Expansionary monetary policy if the Central Bank decided to expand domestic credit increases the money supply.

As a result of this increase in the LM curve shifts to the right. In the new internal balance (B), the balance of payments deficit depreciates the exchange rate.

The economy becomes more competitive and net exports grow, producing two effects: BP moves to the right to the competitiveness and the IS curve shifts to the right by the increase in aggregate demand generated by the devaluation of the currency. This effect is similar for both high and low capital mobility. Expansionary monetary policy produces, therefore, a rise in income, falling interest rates and currency devaluation.

b) Comparative Statics with Perfect Capital Mobility With perfect capital mobility must meet the condition of uncovered interest parity. The arbitration shall ensure that the returns of domestic and international assets are equal. ie

r = r * Ee

To analyze the stability conditions of the model, the equations should be arranged in such a way that the endogenous variables respond positively to excess demand or supply in their respective markets. In the case of goods market, with an excess of demand, the product must increase to restore equilibrium. Then the equation of this market should be sorted in terms of excess demand. The same should be done with the money market equation. To an excess demand for money, the interest rate rises. Finally, the equation of the uncovered interest parity must be ordered in terms of excess demand for domestic bonds. If the nominal yield on domestic bonds less the yield on foreign bonds, emerging capital of the economy and the exchange rate depreciates to balance yields.

(6)

Expansionary Fiscal Policy: Increased Spending on National Assets

In the multiplier matrix can be seen that the increase in spending on goods funded national bonds, raise aggregate demand and therefore the IS curve moves right. Given the excess demand in the goods market, the product increases.

Therefore, the demand for money increases. The excess demand in the money market is eliminated with the rise in domestic interest rates. As the nominal yield on domestic bonds is higher than the nominal yield foreign bonds, capital entering the economy and the nominal exchange rate appreciates.

The lower exchange rate moves up BB Curve and the IS curve to the left.

The effect is a major product, a higher interest rate and a lower rate /change.

Expansionary Monetary Policy

Unlike a system of fixed exchange rate, under a flexible exchange rate monetary policy does have effects on output. The purchase of bonds by the central bank shifts the LM curve to the right, decreasing the rate interest. This decrease, increases aggregate demand and, therefore, the product.

On the other hand, the nominal yield on domestic bonds falls below foreign bond yields, so that the nominal exchange rate rises.

As is true of course that the Marshall-Lerner condition, the trade balance improves. The increase in the exchange rate shifts the arbitration down and the IS curve to the right.

International Shock: increasing the interest rate r *

(7)

What are the effects of an adverse international shock on the product, interest rate and exchange rate? If you raise the international interest rate, bonds foreigners become more profitable, and financial integration curve (BB) will move upwards. Given the resulting outflow of capital, the exchange rate increase and the BB curve will move downwards.

As the devaluation improves the trade balance, according to the Marshall-Lerner condition, aggregate demand will rise, thereby increasing the product. The resulting excess demand for money is removed with a rise in domestic interest rates. The increase in the exchange rate shifts the IS to the right and downward curve arbitrage. In the final equilibrium, the product improves, the interest rate increases and the exchange rate rises.

(8)

Expectations and the Mundell-Fleming Model

a) The course of the exchange rate expected given the effects of changes in the expected exchange rate can also be analyzed from the multiplier matrix. But this does not help to understand why change expectations about the future value of the exchange rate. Consider, first, the effects of fiscal and monetary policies on the endogenous variables under the assumption of a given expected exchange rate. Under this assumption, the equation of the uncovered interest parity can be rewritten as follows:

The current exchange rate (E) is inversely related to interest rate domestic and given E and r *. Therefore, an increase in r will cause a decrease in E, and vice versa:

The model is completed with the equations of the IS and LM curves:

Effects of fiscal and monetary policies

An increase in government spending shifts the IS to IS '. The LM curve is unaffected. The positive effect of increased aggregate demand for the product increases the demand for money which, in turn, generates an upward pressure on interest rates. The increase in interest rate causes an appreciation of the exchange rate and both, decreased demand for goods, offsetting some of the initial expansionary effect of increased spending.

(9)

## CURRENCY PUZZLES

Expansionary fiscal policy increases consumption, but has an ambiguous effect on investment. Moreover, as the exchange rate appreciates, the increase of budgetary trade balance deteriorates. It is important to note, however, that the new equilibrium B is not necessarily stable. Given the deterioration of the trade balance, devaluation expectations should increase. In this case, the curve inversely related interest rate (r) with the exchange rate (E), would shift to the right, from A0 to A1, achieving the balance to the initial level of the exchange rate, but with a higher interest rate.

(10)

(11)

If the government implemented a contractionary monetary policy, the LM curve moves to the left to LM '. The equilibrium moves from A to B with a higher domestic interest rates and a lower exchange rate. The only difference with the expansionary fiscal policy is contractionary monetary policy reduces the product. Both policies, however, increase the interest rate and depress the exchange rate.

In summary, the tight monetary policy reduces private consumption and investment, and trade balance deteriorates. Again, balance B can not necessarily be stable, as devaluation expectations would change the face of deteriorating trade balance or current account.

## Exhibit 1: Factors that Affect Foreign Exchange Rate Movements

## Demand for Currency Price of Currency

National Income Demand for Currency

Real Interest Rates Demand for Currency

Inflation Rates Demand for Currency

National Wealth (Current Account) Demand for Currency

Preferred Currency Mix Demand for Currency

Financial Risk Demand for Currency

Political Risk Demand for Currency

Supply of Domestic Bonds Demand for Currency

Source: Levich (2001)

## ITMEER

In the top panel (with low capital mobility) the new internal equilibrium (point B) is located below the BP curve, ie no internal equilibrium with the external deficit.

As the exchange rate is flexible, it must be adjusted to improve the balance of payments. Indeed, the domestic currency depreciates. Given the Marshall - Lerner condition, the effect of devaluation on aggregate demand is expanding: the IS curve will move again but this time to IS.'' The devaluation will also have the effect of improving the competitiveness of the economy. Consequently, the BP curve will move to the right (BP '). In the final equilibrium (point C) the effects of fiscal expansion would be an increase in real output and interest rate and currency depreciation.

## ARCH/GARCH MODELS

In the bottom pane, point B is on the BP curve in the area of surplus. Type

change must fall to correct this imbalance. With the revaluation of the currency will have two effects: a recession in the real sector that makes the IS curve moves to IS''and a deterioration in external competitiveness caused by the appreciation curve that moves BP to BP. " The final balance model (C) shows a rise in output and interest rates, and an appreciation of domestic currency.

Expansionary monetary policy if the Central Bank decided to expand domestic credit increases the money supply.

As a result of this increase in the LM curve shifts to the right. In the new internal balance (B), the balance of payments deficit depreciates the exchange rate.

The economy becomes more competitive and net exports grow, producing two effects: BP moves to the right to the competitiveness and the IS curve shifts to the right by the increase in aggregate demand generated by the devaluation of the currency. This effect is similar for both high and low capital mobility. Expansionary monetary policy produces, therefore, a rise in income, falling interest rates and currency devaluation.

b) Comparative Statics with Perfect Capital Mobility With perfect capital mobility must meet the condition of uncovered interest parity. The arbitration shall ensure that the returns of domestic and international assets are equal.

To analyze the stability conditions of the model, the equations should be arranged in such a way that the endogenous variables respond positively to excess demand or supply in their respective markets. In the case of goods market, with an excess of demand, the product must increase to restore equilibrium. Then the equation of this market should be sorted in terms of excess demand. The same should be done with the money market equation. To an excess demand for money, the interest rate rises. Finally, the equation of the uncovered interest parity must be ordered in terms of excess demand for domestic bonds. If the nominal yield on domestic bonds less the yield on foreign bonds, emerging capital of the economy and the exchange rate depreciates to balance yields.

Expansionary Fiscal Policy: Increased Spending on National Assets

In the multiplier matrix can be seen that the increase in spending on goods funded national bonds, raise aggregate demand and therefore the IS curve moves right. Given the excess demand in the goods market, the product increases.

Therefore, the demand for money increases. The excess demand in the money market is eliminated with the rise in domestic interest rates. As the nominal yield on domestic bonds is higher than the nominal yield foreign bonds, capital entering the economy and the nominal exchange rate appreciates.

The lower exchange rate moves up BB Curve and the IS curve to the left.

The effect is a major product, a higher interest rate and a lower rate /change.

Expansionary Monetary Policy

Unlike a system of fixed exchange rate, under a flexible exchange rate monetary policy does have effects on output. The purchase of bonds by the central bank shifts the LM curve to the right, decreasing the rate interest. This decrease, increases aggregate demand and, therefore, the product.

## EXCHANGE RATE REGIMES

On the other hand, the nominal yield on domestic bonds falls below foreign bond yields, so that the nominal exchange rate rises.

As is true of course that the Marshall-Lerner condition, the trade balance improves. The increase in the exchange rate shifts the arbitration down and the IS curve to the right.

Expansionary Fiscal Policy: Increased Spending on National Assets

In the multiplier matrix can be seen that the increase in spending on goods funded national bonds, raise aggregate demand and therefore the IS curve moves right. Given the excess demand in the goods market, the product increases.

Therefore, the demand for money increases. The excess demand in the money market is eliminated with the rise in domestic interest rates. As the nominal yield on domestic bonds is higher than the nominal yield foreign bonds, capital entering the economy and the nominal exchange rate appreciates.

The lower exchange rate moves up BB Curve and the IS curve to the left.

The effect is a major product, a higher interest rate and a lower rate /change.

Expansionary Monetary Policy

Unlike a system of fixed exchange rate, under a flexible exchange rate monetary policy does have effects on output. The purchase of bonds by the central bank shifts the LM curve to the right, decreasing the rate interest. This decrease, increases aggregate demand and, therefore, the product.

On the other hand, the nominal yield on domestic bonds falls below foreign bond yields, so that the nominal exchange rate rises.

As is true of course that the Marshall-Lerner condition, the trade balance improves. The increase in the exchange rate shifts the arbitration down and the IS curve to the right.

Expansionary Fiscal Policy: Increased Spending on National Assets

The lower exchange rate moves up BB Curve and the IS curve to the left.

The effect is a major product, a higher interest rate and a lower rate /change.

Expansionary Monetary Policy

Expansionary Fiscal Policy: Increased Spending on National Assets

The lower exchange rate moves up BB Curve and the IS curve to the left.

The effect is a major product, a higher interest rate and a lower rate /change.

Expansionary Monetary Policy

In the top panel (with low capital mobility) the new internal equilibrium (point B) is located below the BP curve, ie no internal equilibrium with the external deficit.

As the exchange rate is flexible, it must be adjusted to improve the balance of payments. Indeed, the domestic currency depreciates. Given the Marshall - Lerner condition, the effect of devaluation on aggregate demand is expanding: the IS curve will move again but this time to IS.'' The devaluation will also have the effect of improving the competitiveness of the economy. Consequently, the BP curve will move to the right (BP '). In the final equilibrium (point C) the effects of fiscal expansion would be an increase in real output and interest rate and currency depreciation.

## CURRENCY CRISES

In the bottom pane, point B is on the BP curve in the area of surplus. Type change must fall to correct this imbalance. With the revaluation of the currency will have two effects: a recession in the real sector that makes the IS curve moves to IS''and a deterioration in external competitiveness caused by the appreciation curve that moves BP to BP. " The final balance model (C) shows a rise in output and interest rates, and an appreciation of domestic currency.

Expansionary monetary policy if the Central Bank decided to expand domestic credit increases the money supply.

As a result of this increase in the LM curve shifts to the right. In the new internal balance (B), the balance of payments deficit depreciates the exchange rate.

The economy becomes more competitive and net exports grow, producing two effects: BP moves to the right to the competitiveness and the IS curve shifts to the right by the increase in aggregate demand generated by the devaluation of the currency. This effect is similar for both high and low capital mobility. Expansionary monetary policy produces, therefore, a rise in income, falling interest rates and currency devaluation.

b) Comparative Statics with Perfect Capital Mobility With perfect capital mobility must meet the condition of uncovered interest parity. The arbitration shall ensure that the returns of domestic and international assets are equal.

## CONTAGION

To analyze the stability conditions of the model, the equations should be arranged in such a way that the endogenous variables respond positively to excess demand or supply in their respective markets. In the case of goods market, with an excess of demand, the product must increase to restore equilibrium. Then the equation of this market should be sorted in terms of excess demand. The same should be done with the money market equation. To an excess demand for money, the interest rate rises. Finally, the equation of the uncovered interest parity must be ordered in terms of excess demand for domestic bonds. If the nominal yield on domestic bonds less the yield on foreign bonds, emerging capital of the economy and the exchange rate depreciates to balance yields.

Expansionary Fiscal Policy: Increased Spending on National Assets

The lower exchange rate moves up BB Curve and the IS curve to the left.

The effect is a major product, a higher interest rate and a lower rate /change.

Expansionary Monetary Policy

Expansionary Fiscal Policy: Increased Spending on National Assets

The lower exchange rate moves up BB Curve and the IS curve to the left.

The effect is a major product, a higher interest rate and a lower rate /change.

Expansionary Monetary Policy

Expansionary Fiscal Policy: Increased Spending on National Assets

The lower exchange rate moves up BB Curve and the IS curve to the left.

The effect is a major product, a higher interest rate and a lower rate /change.

Expansionary Monetary Policy

Expansionary Fiscal Policy: Increased Spending on National Assets

## CONCLUSION

The lower exchange rate moves up BB Curve and the IS curve to the left.

The effect is a major product, a higher interest rate and a lower rate /change.

Expansionary Monetary Policy