# Factors affecting exchange rate

### Introduction

Today the major economies have removed their controls on the movement of capital. As a result the capital has become more mobile. A more mobile capital has undoubtedly affected the value of different currencies and interest rates. When the financial markets became more internationalized it leads to an increase in the amount of capital trying to take advantage of currency swings. The current international monetary system can be described as a hybrid system, where the basic market mechanisms for establishing exchange rates include the free float, managed float, target-zone arrangement and fixed-rate system. This system has led to rapidly fluctuating exchange rates, creating both problems and opportunities for actors dealing with foreign currencies.

During the last two decades a growing number of countries have abandoned their fixed or pegged exchange rate arrangements in favor of more flexible arrangements. In 1984, 21.6% of all countries had managed or independently floating arrangements.

10 years later in 1994 this number had risen to 50.6%. This trend toward greater exchange rate flexibility is a consequence of rising international capital mobility. The rise of the international capital mobility has made it difficult for many governments to defend their fixed or pegged exchange rates or even pursue independent macroeconomic policies.

Theories aiming to explain and understand the interaction of international monetary variables have become increasingly important in the backdrop of the deregulation and international integration of financial markets throughout the world. One theory linking exchange, interest and inflation rates is the International Fisher Effect. It states that the future spot rate of exchange can be determined from the nominal interest differential. The real interest rates will in turn be equalized across the world through arbitrage. This means that the difference in the observed nominal rates will be stemming from differences in expected inflation rates.

### Literature Review

There is conflicting evidence for the International Fischer Effect Parity equality. Aliber and Stickney (1975) calculated the percentage deviation from the Fisher Effect for thirteen countries, constituting both developed and developing countries for the period 1966-71. They concluded that the International Fisher Effect holds in the long run. The maximum annual deviation was however too large to support the theory in the short run. Another study indicating a long-run tendency for interest differentials to offset exchange rate changes were made by Giddy and Dufey (1975). Robinson and Warburton (1980) disputed the validity of the International Fisher Effect. They argued that according to the Fisher Effect the possibility to earn a higher interest return would be eroded in the medium term by the appreciation of the currency with the lower interest rate relatively to the currency with the higher interest rate. They concluded that superior returns could be earned and therefore argued that the International Fisher Effect does not hold empirically. Kane and Rosenthal (1982) studied the Eurocurrency market for six major currencies during the period 1974 to 1979 and their study gave support to the theory of the International Fisher Effect.

Apart from exchange rate differential, several studies have been made in finding factors other than interest rate differential that affects the exchange rate. Charles and Robert have studied the effects of Current Account Balance on exchange rates (Journal of Money Credit and Banking - 1985). Sen and Dua (2006) have examined the relationship between the real exchange rate, level of capital flows, volatility of the flows, fiscal and monetary policy indicators and the current account surplus. The estimations indicate that the variables are co-integrated and each granger causes the real exchange rate.

### Purpose

The purpose of this study is to describe the theory of the International Fisher Effect and test its empirical validity in the long run. Apart from interest rate differential, the report also tries to analyze other factors affecting the spot exchange rate and thereby tries to develop a model that is a better predictor of spot exchange rate than one proposed by the International Fischer Effect.

### Methodology

For studying the International Fischer Effect, a regression model with test of hypothesis using t-test is employed. For improving the model by incorporating other factors other than interest rate differential, multivariate regression is employed. The independent variables under study include Net Current Account flows (Merchandise and Invisibles), Net Capital flow (Foreign Investment + Loans + Banking Capital + Rupee Debt Service + Other Capital), Money Supply and Interest Rate Differential.

The regressions will use Ordinary Least Squares (OLS) estimates.

### Theoretical Framework-International Fischer Effect

The International Fischer Effect can be derived from the Relative Purchasing Power

### Purchasing Power Parity

Purchasing Power Parity (PPP) can be divided into two versions: absolute PPP and relative PPP. The absolute version states that the real price of a good must be the same in all countries. That is, all goods obey the law of one price. The relative PPP is the most commonly used version of PPP and also the one I am referring to when talking about Purchasing Power Parity. The relative version of PPP states that the exchange rate between any two countries will adjust to reflect changes in the price levels of the same two countries. The purchasing parity relation can be written as follows:

Where:

- St is the domestic currency value of one unit of foreign currency at time t
- St+1 is the spot exchange rate at time t+1
- ih,t is the inflation rate at time t in the home country if,t is the inflation rate at time t in the foreign country

The Purchasing Power Parity can also be presented in following approximation:

This approximation relates inflation to exchange rate changes stating that inflation differentials will be offset by exchange rate changes.

### The Fischer Effect

The domestic Fisher Effect is the theory stating that the nominal interest rate r in a country is determined by the real interest rate R and of expected inflation rate over the term of the interest rate E (i) as follows:

As with the PPP there also exists a generalized version of this parity condition. The generalized version of the Fisher Effect states that real returns are equalized worldwide through arbitrage. If the real return is higher in one country than another it would lead to a flow of capital to the country with the higher rate of return until expected real returns becomes equalized. The implicit assumption here is that investors view foreign and domestic assets as perfect substitutes. If capital markets are perfect and capital is completely mobile it will ultimately lead to an equalization of real interest rates across the world. From this follows that in equilibrium, the nominal interest rate differential would approximately equal the expected inflation rate. This is shown in the below equation:

The above can be approximated by the below equation if rh and E (if) are relatively small. By subtracting 1 from both sides and assuming rh and E (if) are relatively small we get:

### The International Fischer Effect

The International Fisher Effect is the international counterpart of the Fisher Effect. It can be seen as a combination of the generalized version of the Fisher Effect and the relative version of the Purchasing Power Parity.

By combining these two equations we get the International fisher relation:

### The Data

Changes on the exchange rates can take place through changes in trade patterns in the goods market, some sort of activity between the goods and money markets or changes in real cross-border investments. From this it can be concluded that the effects on the exchange rates are more likely to occur if free trade is present and the currencies exchange rates are allowed to fluctuate without the intervention of governments. This is why we have chosen to study floating currencies, which are currencies whose value is set primarily by market forces. To study the International Fischer Effect, United States is chosen as the home country. The three foreign countries that are chosen are Canada, Japan and Australia. For all the four countries, there are minimum capital control restrictions. For each country pair (US-AUS, US-CAN, US-JPN), we try to analyze the International Fischer Effect independently. The data consists of quarterly nominal risk free interest rates for four countries and quarterly exchange rates between the US dollar and three other currencies between the years 2001(Q1)- 2009(Q2). As a proxy for risk free rate, the quarterly interbank rates in the four countries are considered for analysis. The exchange rate and interest rate data were obtained from the following OECD data source:

### The Regression Model-International Fischer Effect

The International Fischer Effect equation can be expressed as:

On adding an error term to the equation, the form becomes:

That is, the percentage change in the expected spot rate of exchange should equal the percentage nominal interest differential. Thus, the regression model takes the following form:

We want to reject the International Fischer Effect. As such our null hypothesis is:

A t-test will be applied to ? and ?, whose hypothesized values are 0 and 1 respectively. The regressions use Ordinary Least Squares estimates of Alfa and Beta. Interpreted literally, ? shows the value of the exchange rate change when the nominal interest differential is 0, that is when the nominal interest differential is 0 the exchange rate should not change and hence, also equal 0. When ? equals 1 it means that a 1 percent increase in the nominal interest differential will lead to a 1 percent offsetting change in the exchange rate. That is, if the nominal interest rate is one percent higher in the United States than in the foreign country, the US dollar will depreciate by one percent relatively to the foreign currency.

The nominal interest differential has been computed by taking the US nominal interest rate minus the foreign nominal interest rate divided by one plus the foreign nominal interest. The exchange rate change contains the exchange rate change from one quarter to another where the exchange rate is expressed as foreign currency units per US dollar. It has been computed by taking the exchange rate at time t+1 minus the exchange rate at time t, divided by the exchange rate at time t. These figures will then be compared. For instance, the nominal interest differential in the first quarter of 2002 between the United States and Japan is compared and contrasted to the exchange rate change of the Yen/US dollar between the first and second quarter of 2002. These nominal interest differentials should, according to the International Fisher Effect, on average be offset by exchange rate changes. This proposition is tested.

### The Regression Model - Multivariate Analysis

After analyzing the International Fischer Effect, the Multivariate analysis tries to improve the predicting power of the spot exchange rate by including factors other than interest rate differential. This includes the following independent variables which are included in the model:

St+1 = a + b*CAPt+1 + c*CURt+1 + d*MSt+1 + e*IRDt+1

Where a, b, c, d and e are regression co-efficient

- St+1 = Spot Exchange in period t+1
- CAPt+1 = Net Capital Account inflow for period t+1
- CURt+1 = Net Current Account Flows for period t+1
- MSt+1 = Money in Circulation in period t+1
- IRDt+1 = Interest rate differential for period t+1 = [(rh,t - rf,t) / (1 + rf,t)]*St + St

In this case, we study the Re-$ exchange rate. The time period under study is 2001(Q2) to 2008(Q2). The quarterly Net Capital Flow, Current Account flow, Money Supply and interest rate data are collected for the periods which are the independent variables in the regression model.

### Limitations of the Analysis

- Since we are comparing all countries to the US dollar there is a risk that the result would be country specific. This problem can of course be avoided by choosing more than one home country.
- Another methodological problem is that we might get a time specific result.

The result might only be valid or not valid during the chosen time frame. This might be avoided by choosing more than one time period.

### Regression Results and Analysis

The regression results for United States-Canada

The regression from US- Canada gave the following outcome: Regression Equation:

Y= a + ß X

Where, Y= Exchange Rate between the US-Canada

- X= Interest Rate differential
- R-squared = 0.015
- Constant a = -0.009
- Variable ß = -0.589

The acceptance region at a 5% significance level for a is -0.026< a < 0.008. The acceptance region at a 5% significance level for ß is -2.321 < ß < 1.143. Durbin Watson Statistic: 1.410

VIF: 1.00

The R-squared tell us how much of the variation in the dependent variable the explanatory variable can explain. The R-squared for US-Canada turned out to be very low. Only 1.5% of the quarterly changes in the Canadian$/US$ exchange rate can be explained by the nominal interest differentials. This leaves 98.5% of the quarterly changes in the exchange rate to be explained by other factors.

The null hypothesis that a = 0, ß = 1 will be rejected if the hypothetical values of a and ß lie outside their respective acceptance regions. We must, however, be cautious in our conclusions due to the low R2, which indicates that the model's overall performance is low. However, both a and ß lie within their acceptance regions at 5% significance and H0 cannot be rejected. This means that we can be 95% confident that the true values of a and ß lie somewhere inside their respective acceptance regions. Thus International Fischer effect is holding true for US Canada. The result also illustrates that a 1% increase in the nominal interest differential, on average, lead to approximately a 0.5% offsetting change in the Canadian$/US$ exchange rate i.e Canadian $ depreciates by 0.5% against the US$. The a- value, in turn, says that if the nominal interests in the United States and Canada are the same, the change in the exchange rate would on average equal 0.1%. This is practically the same as a no change.

The Durbin Watson statistic comes out to be 1.410 which is within the acceptable range of -2 to +2 indicating no autocorrelation between the error terms.

The regression results for United States-Japan The regression from US- Canada gave the following outcome: Regression Equation:

Y= a + ß X

Where, Y= Exchange Rate between the US-Canada

- X= Interest Rate differential
- R-squared = 0.075
- Constant a = -0.021
- Variable ß = 0.666

The acceptance region at a 5% significance level for a is -0.046< a < 0.004

The acceptance region at a 5% significance level for ß is 0.193 < ß < 1.525

Durbin Watson Statistic: 1.882

VIF: 1.00

The R-squared tell us how much of the variation in the dependent variable the explanatory variable can explain. The R-squared for US-Japan turned out to be quite low. Only 7.5% of the quarterly changes in the Japanese Yen/US$ exchange rate can be explained by the nominal interest differentials. This leaves 92.5% of the quarterly changes in the exchange rate to be explained by other factors.

The null hypothesis that a = 0, ß = 1 will be rejected if the hypothetical values of a and ß lie outside their respective acceptance regions. However, both a and ß lie within their acceptance regions at 5% significance and H0 cannot be rejected. This means that we can be 95% confident that the true values of a and ß lie somewhere inside their respective acceptance regions. Thus International Fischer effect is holding true for US Japan. The result also illustrates that a 1% increase in the nominal interest differential, on average, lead to approximately a 0.66% offsetting change in the Japanese Yen/US$ exchange rate i.e Japanese Yen appreciates by 0.66% against the US$. The a- value, in turn, says that if the nominal interests in the United States and Japan are the same, the change in the exchange rate would on average equal -0.021%.

This is practically the same as no change.

The Durbin Watson statistic comes out to be 1.882 which is within the acceptable range of -2 to +2 indicating no autocorrelation between the error terms

The regression results for United States-Australia The regression from US- Australia gave the following outcome: Regression Equation:

Y= a + ß X

Where, Y= Exchange Rate between the US-Australia

- X= Interest Rate differential
- R-squared = 0.012
- Constant a = -0.025
- Variable ß = -0.006

The acceptance region at a 5% significance level for a is -0.084< a < 0.035

The acceptance region at a 5% significance level for ß is -0.027 < ß < 0.014

Durbin Watson Statistic: 1.462

VIF: 1.00

The R-squared for US- Australia turned out to be exceptionally low. Only 1.2% of the quarterly changes in the C$/$ exchange rate can be explained by the nominal interest differentials. The main part of the quarterly exchange rate changes between the Australian $/US $ would be better explained by other factors than the nominal interest differentials.

Here we can also reject the null hypothesis that a = 0, ß = 1 since the hypothetical value of ß lies outside the acceptance region at 5% significance. Thus International Fischer effect is not holding true for US Australia. We must, however, be cautious in our conclusions due to the low R2, which indicates that the model's overall performance is low. The result illustrates that a 1% increase in the nominal interest differential leads to a 0,157% change in the Australian$/US$ exchange rate. This number is far from what's predicted by the theory, which stated that the prediction errors would cancel out over time, resulting in a Beta value of 1. However, the Alfa value of 0,006178 can be considered to be insignificant different from zero.

### The Regression results for United States-India

The regression from US- India gave the following outcome: Regression Equation:

Y= a + ß X

Where, Y= Exchange Rate between the US-India

- X= Interest Rate differential
- R-squared = 0.122
- Constant a = -0.020
- Variable ß = -0.700

The acceptance region at a 5% significance level for a is -0.046< a < 0.005. The acceptance region at a 5% significance level for ß is -1.402 < ß < 0.001.

Durbin Watson Statistic: 1.204

VIF: 1.00

The R-squared tell us how much of the variation in the dependent variable the explanatory variable can explain. The R-squared for US-India turned out to be low. Only 12.2% of the quarterly changes in the Canadian$/US$ exchange rate can be explained by the nominal interest differentials. This leaves 87.8% of the quarterly changes in the exchange rate to be explained by other factors.

Here we can also reject the null hypothesis that a = 0, ß = 1 since the hypothetical value of ß lies outside the acceptance region at 5% significance. Thus International Fischer effect is holding true for US India. We must, however, be cautious in our conclusions due to the low R2, which indicates that the model's overall performance is low. The result illustrates that a 1% increase in the nominal interest differential leads to a 0.700% change in the US$/Rupees exchange rate. However, the Alfa value of 0.020 can be considered to be insignificant different from zero.

The Durbin Watson statistic comes out to be 1.204 which is within the acceptable range of -2 to +2 indicating no autocorrelation between the error terms Since for India Capital account is not convertible there are barriers to flow of capital in and out of the country. As such interest rate differential is not the sole predictor of exchange rate fluctuation. Other factors like net current account flow, net capital account flow, money supply together with interest rate differential are used as independent variables in multivariate regression analysis to predict the spot exchange rate. The following section outlines the regression results.

The Regression results for United States-India including other factors The regression from US-India gave the following outcome: Regression Equation:

Y= a + ß1 X1 + ß2 X2 + ß3 X3 + ß4 X4

Where, Y = Exchange Rate between the US-India

- X1 = Net Current Account X2 = Net Capital Account X3 = Money Supply
- X4= Interest Rate Differential
- R-squared = 0.915
- Constant a = 22.827
- Variable ß1 = -0.8227

The R-squared tell us how much of the variation in the dependent variable the explanatory variable can explain. The R-squared for US-India turned out to be high.

91.5% of the quarterly changes in the US$/Indian Rupees exchange rate can be explained by the nominal interest differentials. This leaves only 8.5% of the quarterly changes in the exchange rate to be explained by other factors.

Various possible real exchange rate determinants for India are regressed. Net Current Account has a low t-value and Level of Significance of 43.33% indicating that it is not a good predictor for Exchange Rate. Money Supply, Net Capital account and Interest rate differential have high t-values at 95% level of confidence. These high t- values indicate a high explanatory power of these independent variables.

VIF values for all independent variables are between 1-10 indicating no multi- collinearity.

The Durbin Watson statistic comes out to be 1.690 which is within the acceptable range of -2 to +2 indicating no autocorrelation between the error terms.

### Conclusion

The purpose of this thesis was to describe the theory of the International Fisher Effect and test its empirical validity in the long run. Employing regression analysis to nominal interest differentials and exchange rate changes made this possible. The result from the regressions generated following conclusions.

The R-squared turned out very low for all country pairs. Because the R2 is low for all studied country pairs, the nominal interest differentials should not be used to predict changes in future spot rate on a quarterly basis. This is also in line with the theory, stating that the nominal interest differentials are not a particularly accurate predictor of short-run movements in the spot rate of exchange. The low R2 is also indicating that the model's overall performance is low.

The hypothetical values of a and ß all lie in their respective acceptance regions at 5% significance for US-Canada and US-Japan. Therefore, the null hypothesis that a = 0, ß = 1, cannot be rejected for these country pairs. This means that we can with 95% certainty say that the true values of a and ß lie somewhere in their respective acceptance regions. So, International Fisher Effect holds true for US-Canada and US- Japan.

However, we can reject the null hypothesis for US-Australia and US-India, since the hypothesized values of ß for these country pairs lie outside respective acceptance region. Though, we must be careful in our conclusions due to the low R2, which indicates that the model's overall performance is low. Nevertheless, if we reject the null hypothesis for US-Australia and US-India we can conclude that the Beta-value cannot equal 1 for these country pairs, and therefore we cannot expect the nominal interest differentials to be fully offset by exchange rate changes for these pair of countries. This is also indicated by the low estimates of ß for these country pairs, with ß=-0.006 for US-Australia.

Another explanation for the rejection of the null hypothesis might be the low explanatory power of the R-squared, indicating that the model's overall performance is low. The regressions for US-Australia and US-India resulted in R-squared of 1.22% respectively 12.22%. Such low estimates might indicate that the nominal interest differentials do not influence the exchange rate changes linearly and as a consequence, being a contributing cause for the rejections of the null hypothesizes. However, the estimates of a for the different country pairs resulted in values insignificant different from its hypothesized value of zero. Thus, on average, we could expect the exchange rate to remain unchanged when the nominal interest differential equals zero.

The low Beta values show that the exchange rate movements react to other factors in addition to nominal interest differentials. This might also indicate that the money markets are not truly internationalized. There are many restrictions that prevent capital from freely flowing across borders to directly match nominal interest rate differentials. Examples of such factors are political risk, currency risk, transaction costs, taxes and psychological barriers. Though, one could assume factors like political risk to be insignificant for the investigated countries during the studied time frame. The exchange rate changes can also come about through some sort of activity between the goods and money markets, some real cross-border investment activity or change in trade patterns in the goods market, that all in all, still indirectly ensure nominal interest differentials are still, on average, offset by exchange rate changes. However, neither can the International trade assumed to be free. One could also expect slow adjustments in the goods markets and/or investments activities relatively to the money markets, why one might not see the effect on exchange rates by studying quarterly data.

### Conclusion for India US analysis

For US-India pair Regression analysis was then done with other possible exchange rate determinants i.e net current account, net capital account and money supply. Results showed that Exchange rate was determined by the Capital account, money supply in the system and the interest rate differentials between India and US. This could be explained by the fact that India is Current account convertible but has capital controls. Therefore exchange rate in India depends on net capital account transactions, money supply and interest rate differential between India and the respective country. From the results, it is observed that Current Account deficit is not a significant predictor of exchange rate fluctuation in the near term. On doing literature review, we found that Current Account deficit is a predictor of exchange rate fluctuation only in the long term. Here we are considering only the quarterly exchange rates for last 8 years. Ideally to get significant relationship data for more than 25 years should be selected and as such it is not a good predictor in the near to medium term.

### References

### Internet:

- http://www.wikipedia.org
- http://www.rbi.org.in
- http://www.economist.com
- http://www.stats.oecd.org

### Journals:

- Kohli Renu (2003), "Capital Flows and Domestic Financial Sector in India",
- Economic and Political Weekly, pp. 761-767.
- Chakraborty Indrani (2003), "Liberalization of Capital Inflows and the Real Exchange
- Rate in India: A VAR Analysis", IMF Working Paper, No. 351.