The Modelling Exchange Rate Determination

Published Date: 02 Nov 2017

CONTENTS

ABSTRACT

LIST OF FIGURES

LIST OF TADLES

LIST OF ABBREVIATIONS

INTRODUCTION

CHAPTER 1 DEFINING THE EXCHANGE RATE

1.1 Nominal exchange rate

1.2 Real exchange rate

CHAPTER 2 MODELLING EXCHANGE RATE DETERMINATION

2.1 Purchasing Power Purity

2.2 Monetary Models

2.2.1 Flexible-Price Monetary Model

2.2.2 Sticky-Price Monetary Model

2.2.3 Model Specification

CHAPTER 3 ECONOMETRIC METHODOLOGY

3.1 Time series and stochastic processes

3.2 Test for normality

3.3 OLS regression

3.4 Test for ARCH

3.5 Test for GARCH

CHAPTER 4 ESTIMATION RESULTS

4.1 Data

4.2 Testing for unit roots

4.2.1 Unit root test procedure

4.2.2 ADF testing

4.3 Test for normality

4.4 OLS regression results

4.5 Test for ARCH

4.6 Test for GARCH

CONCLUSION

Bibliography

Appendix

CHAPTER 1 DEFINING THE EXCHANE RATE

1.1 Nominal Exchange Rate

The nominal exchange rate represents the price of a domestic currency measured in terms of a foreign currency. It indicates how much foreign money units would be received for a domestic money unit (or vice versa), but it does not show the purchasing power of neither currencies. The Central Bank (CB) expresses the nominal exchange rate with an official quote which is always shown bilaterally in a pair'. This results from the fact that in every foreign exchange (FX) transaction, there is simultaneously buying of one currency and selling of another. The bilateral nominal exchange rate is established on the FX market as a result of matching demand and supply, or via interbank transactions. In this latter case, the CB acts usually as one of the counterparties of this relationship (Piana, 2001).

The FX rate can be expressed in two ways, every time in which the first currency would represent the base for the trading. It is a constant - always set to be equal to 1. The second currency is called "term"," counter", "payable" or "quote", because it varies during the time. The only two possible quotations are:

Direct (also called American) - the domestic currency is expressed per unit foreign currency

Indirect - how many units of foreign currency are used for the purchasing of one unit domestic currency.

Their relationship is expressed below.

Indirect quotation = Direct quotation-1

The FX market has no natural numeraire currency. Therefore, there are no strictly defined rules for determining the order of quotation. This choice is purely market convention (Clark, 2011) and depends on the CB's preferences of how to express the domestic currency. It can be argued, that the indirect quotation is more practical. Considering Occam's razor [1] principle, holding the domestic currency as base per se, provides a direct insight of how its relative value changes over time. Another benefit of using the indirect quoting is that it allows an instant conversion of financial results into domestic currency unit, i.e. all business profits and losses are directly priced into home money.

Real Exchange Rate

The real exchange rate (RER) between two countries represents the combined values of all domestic against foreign production at the prevailing (nominal) FX rate. Stated differently, the RER measures the rate at which all home goods and services can be traded relative to the foreign ones. Expressed in formula, this relationship would be as follows:

where q – the RER;

s – the nominal exchange rate;

p and p* – the relative price of domestic and foreign consumption baskets.

The RER's crucial difference with the nominal exchange rate lies within the observed item of trade. In this case, the buyer is interested in what can be bought with the purchased currency. Thus considering the RER, it is not the currency itself, but the prices of foreign goods per domestic ones (Mankiw, 20ii).Therefore, higher domestic prices would mean an appreciation in the RER of the home currency, other things equal (Piana, 2001). This observation is valid for higher nominal exchange rate as well.

The correctly priced RER is essential. When the RER diverge, the currencies also face pressure to change. It is often the case that significantly deviated currencies tend to be pressed to shift in an opposite direction (overvalued currencies depreciate, whereas undervalued- appreciate). In reality, there are some major factors like transportation, trade tariffs, and government policies etc. that impact greatly the FX and RER rates, and therefore, disrupt a potential straight price comparison (Catao, 2007). These expenditures shift additionally a currency away from its equilibrium level, which could incorrectly set its purchasing power and the prices in a country as a whole.

The RER between two countries could also be measured by only a single good in order to minimize the effects of the above-mentioned disturbances. It, however, must be an offered by only one company product which is widely traded and also relatively standardized on the different geographical markets. A suitable good that fulfills all these assumptions is the Big Mac751 burger. It represents a standardized bundle of ingredients, offered in an identical version by only one producer in 120 countries worldwide. This particular good may be regarded as a palatable purchase power measurement tool (Pakko & Pollard, 2002).

The Big Macâ„¢ Index was introduced for the first time in 1986 by the British magazine "The Economist". Ever since, it is published annually as a comparison of Big Mac751 burger's prices in various countries worldwide. In this way, it allows a systematic evaluation of the prevailing RERs. The Big Macâ„¢ Index is based on the purchasing power parity (PPP) concept. It states that in a long-run the RER should adjust to one price between the countries, all things equal. Thus, a burger expressed in a single currency is expected to cost the same on both markets in consideration. It is assumed that the concept of PPP holds true in such an ideal one-product-world where prices represent the exchange rates and the RER equals 1.

This one-product-world is oversimplified. In reality, countries produce and export more than one good. When the whole economy is taken into account, the items of interest would not be individual prices but their constituting price indices. These consumer baskets usually contain the very basic goods and services of the households. Their comparison tracks the price movements, expressed in consumer price index (CPI), among different countries. Measuring the RER in indices is a very flexible procedure. At any given moment in time, it allows benchmarking of overall price changes relative to a base year. In this perspective, it differs from the Big Macâ„¢ measurement which provides only an absolute price comparison. The concept of relative PPP holds true when the RER between countries do not change over time. If the average prices grow linearly, the constituting RER indices should also increase accordingly during the observed time span in order to justify the PPP (Catao, 2007).

The RERs have a significant impact on global markets. More precisely, the RER is a key determinant of the international trade. It impacts the net exports and therefore the trade account of a country. For example, considering Canada as a home region when the Canadian dollar depreciates, domestic goods become cheaper than the imported ones. This leads to an increased consumption of local products at home, as well as abroad.

Due to the two-fold correlation, the demand of US products inevitably decreases. As a result in Canada, the imports fall and the exports rise, which leads to an increased net Canada’s current account (CA). This is a consequence of the Marshall-Lerner condition which states that a change in the domestic currency rate would haw a positive effect on the trade balance only if the sum of the price elasticity of the export and import (in an absolute values) are greater than 1.

Andrew Rose (1991) proposes the so-called imperfect substitutes model in order to view the FX effects on the trade flows. It is a "two-country-trade model" that considers imported and domestic products as imperfect substitutes. Although in his analysis Rose (1991) estimates the partial derivatives when holding real incomes constant, he cannot reveal any strong short-run relationship between exchange rates and the trade balance. However, he is also unable to reject the hypothesis that the generalized Marshall-Lerner condition does not hold in medium- or long-term.

CHAPTER 2

MODELLING EXCHANGE RATE DETERMINATION

Exchange rates are shown to be one of the most difficult and challenging economic variables to properly predict. There is a plethora of forecasting models ranging from the simplest ones to the most sophisticated and complex ones with varying predictive power and quality. Some of models do well and others do not. Among all theories of exchange rate determination, PPP and monetary models have generated a vast amount of literature an empirical results. Nevertheless, results have been differing and sometimes, even questionable. This chapter examines the theory and empirical evidence of PPP and monetary models.

2.1 Purchasing Power Parity

Purchasing Power Parity (PPP) is a theory of determination of the exchange rate. It avouch that exchange rate between two currencies in any point of time is defined by the changes in price levels in two countries. This theory states that the dominant determinant in the exchange rate determination is changes in price levels; and it is also known as "inflation theory of exchange rates".

Interpretation of PPP theory can be traced to 16th century in England and Spain; nevertheless, a Swedish economist Gustav Cassel (1916), was whose who popularized the use of PPP. In 1918, G. Cassel ascertained that in the short term exchange rate would deviate from PPP and identified 3 disturbances (barriers to trade, actual and expected inflation and shifts in international capital movements) which might have caused these deflections.

There are few reasons why deflections from PPP occur. First of all, there might be limitations on trade and capital movements or transfer pricing in a country which will distort the relationship between home and foreign prices. Second reason is official intervantion and speculative activities, which may create a PPP disparity. And in the end,the productivity bias, the case when growth in productivity in the tradable sector is faster in comparison with non-tradable sector, this will result in systematic divergence of internal prices (Balassa, 1964).

The basic concept underlying PPP is that arbitrage forces will equalize prices of goods internationally if they are measured in the same currency. The following forms of PPP are absolute and relative. In the absolute form of PPP, the nominal exchange rate is defined by the domestic and foreign prices ratio. The equation is following:

S=P/P*

where S is the exchange rate, that measured as the price of domestic currency per one unit of foreign currency; P and P* are the domestic and the foreign prices respectively. After taking logarithms of previous equation, the absolute PPP can be written down as:

s_t=p_t-p_t^* (2)

where the lowercase notations denote logarithms of the variables. The absolute version of PPP is highly unlikely to hold because of the existence of transportation costs, imperfect information and the distorting effects of tariffs and protections. Thus, it is argued that a weaker relative version of PPP, known as the relative PPP, can be expected to hold even in the face of these distortions. The relative version of PPP dictates that the percentage change in the exchange rate is equal to the difference in the inflation rates between the two countries. That is,

(3)

where %S is the percentage change in exchange rate, %P is the domestic inflation rate and %P* is the foreign inflation rate. For empirical testing purposes, we can estimate equation (3) by the following,

(4)

where lowercase notation imply logarithms of the variables.

Empirical studies have yielded mixed results for the support of PPP. McNown and Wallace (1989) tested PPP for Argentina, Brazil, Chile and Israel for the 1970s and 1980s and found support for PPP. On the other hand, Bahmani-Okolee (1993) found that PPP holds for only four out of twenty-five developing countries.

Although there are disputes on the validity of PPP as a short-run relationship, there seems to be a general agreement that PPP will hold in the long-run. Thus, if a long-run relationship exists, then logarithms of the nominal exchange rate and the price level indices should move together over the long-run.

Cointegration is a technique to determine whether two or more time series have a long-run relationship. It allows the long run relationship between exchange rates and relative prices to be tested independently of short-run fluctuations. Firstly, there is a need to establish the order of integration for the time series of the exchange rate and prices.

The exchange rate and relative prices are said to be stationary, if they tend to constantly return to their means even though they fluctuate around their means. The test of the order of integration can be found by the following equation for each of the variables,

DXt = bo + b1Xt-1 + gik= å1iDXt-i + mt (5)

where D is the first difference operator.

If b1 < 0, then Xt is stationary. If b1 = 0, then Xt is non-stationary. The hypothesis is that b 1 = 0 is tested by t-ratio. The ratio is an Augmented Dickey-Fuller (ADF) if some lags are required on the right hand side to make the residuals, mt, white noise (i.e. k ³ 1). It is a Dickey-Fuller (DF) test if no lags are required (i.e. k = 0). No equilibrium will exist between variables that are integrated of different orders. As far as PPP theory is concerned, if the exchange rate and relative prices have a long-run relationship, they should have the same order of integration.

Next, based on the Engle-Granger two-step method, the dependent variable (that is, the exchange rate) is regressed on the independent variables (e.g. relative prices). The test of cointegration involves testing whether the residuals from the regression are white noise. That is, we regress st on (pt-p*t),

st = a + b(pt - p*t) + et (6)

and subject the residuals to a stationarity test of white noise.

If the residuals are white noise, then the hypothesis of non-stationarity can be rejected and we can reject the null hypothesis of no cointegration; a long-run relationship exists between exchange rate and relative prices.

In the second step (after establishing a long-run relationship) there may exist an error-correction mechanism (ECM) where short-run dynamics are captured. It takes the form,

Dst = go + g1(Dpt - Dp*t) + g2et-1 + mt (7)

where g2et-1 is the estimated residuals from equation (6) lagged by one period and mt is the white noise error.

The coefficient g2 measures the speed of adjustment to the long-run equilibrium. The error-correction model is valid, conditional on the existence of cointegration between exchange rate and relative prices.

Kim (1990) found, using the Engle-Granger method, that in most cases CPI and WPI are cointegrated with the exchange rate at 5% level. Their data are annual figures for Canada, France, Italy, Japan and the UK. Specifically, Abeysinghe & Lee (1992) also found evidence that the Singapore-US bilateral exchange rate is in agreement with PPP for the period of 1975 Quarter 1 to 1993 Quarter 3, when CPI indices are used.

2.2 Monetary Models

The monetary models of exchange rate start from assumption of perfect mobility of capital. PPP and interest rate parity theorems are used in the models to define the equilibrium conditions. Bonds (domestic and foreign) are assumed to be perfect substitutes. In this chapter, we focus on monetary models, namely the Flexible-Price Monetary Model, Sticky-Price Monetary Model.

2.2.1 The Flexible-Price Monetary Model

The flexible-price monetary model is based on assumption that not only is there no barriers (such as capital control or transaction costs) segmenting international capital markets, but domestic and foreign bonds are also perfect substitutes in investor demand functions. Basically, there is only one bond in the world. Model define analogous assumption for goods market which states that not only are there no barriers (such as trade controls or transportation cost) segmenting international goods markets, but domestic and foreign goods are also perfect substitutes in consumer demand functions. Basically, there is only one good in the world. This assumption suggests purchasing power parity: domestic price level is equal to the foreign price level times the exchange rate (Jeffrey A. Frankel, 1976).

The fundamental equation in the monetary approach is a convectional money demand function:

, (1)

where

m – log of the domestic money supply,

p – log of the domestic price level,

y – log of domestic real income,

i – the domestic nominal interest rate,

ϕ – the money demand elasticity with respect to income,

λ – the money demand semielasticity with respect to the interest rate.

Money demand function for foreign country is similar:

, (2)

where foreign variables are denoted by asterisks.

Taking the difference of equation (1) and (2) gives a relative money demand function:

. (3)

Assumption that domestic and foreign bonds are perfect substitutes gives us uncovered interest parity:

(4)

where - is the expected depreciation of domestic currency.

The one-good assumption gives us PPP:

, (5)

where s is the log of exchange rate defined as the domestic currency units per unit of foreign currency.

Substituting equation (1) and (2) into (4) gives,

(6)

The nominal interest rate is consist of two components, namely real interest rate, and expected domestic and foreign inflation rate.

(7)

(8)

Assuming that real interest rates are equal in both countries, we get following equation:

, (9)

The equation (6) can be rewritten as:

, (10)

The equation (10) is the Flexible-Price Monetary Model. The coefficient of the relative money supply is positive and equal to 1 based on the neutrality of money. Equation states that exchange rate, as the relative price of currency, is determined by the supply and demand for money. Increasing in the supply of domestic money leads to proportionate depreciation. Increasing in domestic income, or reduction in the expected inflation rate, raises the demand for domestic money and thereby causes an appreciation.

2.2.2 The Sticky-Price Monetary Model

Frankel (1979) developed a sticky-price monetary model of the exchange rate. As mentioned, purchasing power parity may be a good approximation in the long run, but large deviations appear in the short run empirically. The existence of imperfect information, contracts, and inertia in consumer habits means that prices do not change instantaneously but adjust gradually over time. Frankel assumed that the expected rate of deprecation of the exchange rate is a positive function of the gap between the current exchange rate and the long-term equilibrium rate, and the expected long-term inflation differential between domestic and foreign countries. This gives the following equation:

, (11)

where δ is the speed of adjustment towards equilibrium. The equation states that the current exchange rate is expected to return to its long-term equilibrium at the rate of δ. In the long-term . Combining equation (7), (8) and (11) gives us following:

(12)

Equation (12) shows that the gap between the current exchange rate and its long-term equilibrium exchange rate is proportional to real interest differentials between the two countries. Thereby, if the foreign real interest rate is higher than domestic real interest rate, then there will be capital outflows from domestic bonds to foreign bonds until the real interest rates are become equal.

The long-term PPP relationship in this model is represented by:

(13)

In the long-term the interest differential must be equal to the long-term expected inflation differential,

(14)

Thus equation (12) can be rewritten as:

(15)

Combining equation (6), (14) and (15) gives us:

(16)

The short-term dynamics of the sticky-price monetary model is obtained by substituting equation (16) into (15) which gives the sticky-price monetary model of Dornbush (1976) and Frankel (1979),

or

(17)

According to equation (17) the signs of the coefficients of and are the same as for flexible-price monetary model. The coefficient is negative. An increasing in domestic interest rate leads to capital inflow, which increases demand for domestic currency and, in turn, leads to the appreciation of domestic currency.

2.2.3 Model specification

Based on monetary models, which were observed above, working model for thesis was specified as follow:

,

where

, - domestic and foreign money market rates, respectively;

, - domestic and foreign short-term interest rates;

, - domestic and foreign consumer price indices.

Time frame

All time-series, used for performing this econometric study, are in monthly frequencies for the period from 1995 to 2012. Chosen time frame involves two financial crises, namely Asian financial crises in 1997-1998, which raised fears of a worldwide economic meltdown, and global financial crisis started in 2007, which is estimating as the worst financial crisis since the Great Depression of the 1930s. It gives opportunity to observe exchange rate behavior during economic cycle: expansion, crisis, recession, and recovery (according to J. Schumpeter) and estimate crises’ influence on it. One more reason for this particular period is data availability. It is trouble to find appropriate and hard data for very long period of time as statistical analysis requires for acceptable and significant results as much observation as possible. Our time frame consists of 212 observations.

The CAD/USD currency pair

The CAD/USD currency pair was chosen due to few factors. Firstly, rapid US dollar depreciation against Canadian dollar lasted from August 2002 to October 2007. This decreasing is approximately 39%, what attract attention. Secondly, Canada and the USA close location towards each other but separated from Europe and Asia. It created special relation between these countries, such as trade partnership. However, import from US as well as export to US has decreasing tendency and only last two years it is stable. Figure below shows percentage of Canadian import/export in comparison with total amount.

Source: Government of Canada

In additional, the CAD/USD takes 5th place in currency distribution of global foreign exchange market turnover, according to the Bank of International Settlements (BIS) triennial survey (2010). It consist 5% of the entire 4 trln USD daily turnover. Thereby, its volume equals 182 bn USD every trading day. The total daily turnover increased from 1.2 to 4 trln US dollar during 2001-2010, it is more than 300%. The USD is contained in 84.9% of all transactions. This percentage decreased as compared with 86.8% in 1998. A percentage share of Canadian dollar is 5.3% in comparison with 3.5% in 1998. Thus, their combined share of all foreign exchange market turnover is 90.2% (out of 200% as each transaction involves two currencies). Figure shows the plotted CAD/USD nominal exchange rate:

GDP and Interest rates

The Gross Domestic Product (GDP) is one of the components of monetary model, and thus, equilibrium exchange rate's determinants. As the value of the total output of goods and services, it represents a measure of the economic activity in a country. The domestic markets are in equilibrium when nationally produced output equalizes the existing demand in the market. This relationship is expressed in equation below:

This equation states that the gross domestic output Y is dependent on consumption of the population C, investments in the economy I, state spending G and net difference between imports and exports NX = IM — X.

Investments are influenced positively by the output. This impact results from the substitution of consumer goods with capital goods, which would optimize further the process of production. On the other hand, increased interest rates may hinder the investment process within the country. They may make the borrowing on the interbank market more expensive, and therefore, the lending to customers may decrease (Hasset, 2008). Higher interest rates may also raise the costs of investing in this particular country in comparison to the rest countries with similar profile but lower interest rates. Investments both domestic and foreign would decrease; therefore the output would be reduced, consequently, the exchange rate decreases.

There is never a simple relationship between interest and exchange rates. The FX rate is influenced by expectations about future interest rates and by any unexpected current change. Provided that investors expect the interest rates to rise, they may increase the amount they invest in a currency before this actually occurs. This would result in an appreciation of the exchange rate of the home currency (Brooks, 2002). Thus, i is viewed as an exogenous variable which affects the RER via its effect on the demand for money. The (i - i*) differential may affect the exchange rate in two ways. Therefore, its sign has to be determined empirically similar to the money supply variable.

Imports, as part of the net import-export balance, are correlated positively with the home output and the RER An increase in the value of the home currency will reduce the price of imports and this will have a direct influence on inflation as many imported goods are included in the CPI. In addition, a higher local currency will tend to reduce the demand abroad for home goods and services, which, in turn, will reduce output.

Exports, on the other hand, depend positively on the foreign output and negatively on the RER If there is a reduction of the domestic demand, it would trigger a decrease in the output, which would in its turn, result in decreased exports. This may shift the demand towards foreign products, especially when there is an increase in the domestic RER. The domestic currency will be stronger, implying more imported goods. The citizens would be willing to consume cheaper foreign products, instead of buying the more expensive home production.

CHAPTER 3 EXCHANGE RATE AND MONETARY POLICY IN CANADA

Since the early 1970s, however, Canada has participated in a floating (or flexible) exchange system in which the price of its currency is dictated, in large part, by currency exchange markets. A currency exchange market is a stock market for national currencies. It is where governments, state banks, commercial banks, multinational corporations, and currency speculators go to buy and sell different national currencies. Moreover, as in any open market, the value of currencies is determined in large party by the economics of supply and demand. When demand is high and supply is low, the price of a currency will tend to rise. In contrast, when demand is low and supply is high, the price will tend to fall.

Today, most governments, including Canada’s, allow international currency markets a large role in determining the exchange rates of their currency. This sort of exchange rate system is referred to as "floating the currency," hence the reason for the term "floating exchange system." This does not mean that governments are complete bystanders in the modern exchange system. The Canadian government, for example, may still intervene in currency markets to moderate sharp market shifts or to pursue limited economic or financial goals. Nevertheless, Canada no longer attempts to keep its currency "fixed" at a particular rate relative to the currencies of other countries.

3.1 Market Influences on the Canadian Dollar

3.1.1 Business Activity in the Canadian Economy

One of the most important forces affecting the supply and demand for the Canadian dollar is the general level of business activity in the economy. Increases or decreases in the level of business activity, relative to other national economies, can often have a corresponding impact on supply and demand for the dollar and its value relative to other currencies. When business activity increases (there are more businesses operating, producing and selling more goods and services, and employing more workers), demand for the Canadian dollar rises in order to cover the higher levels of activity. If supply is not adjusted accordingly, then the price of the dollar relative to other currencies may also increase. Similarly, if the level of business activity decreases, then demand for the Canadian dollar follows suit. If the supply is not adjusted accordingly, then the value of the dollar may fall relative to other currencies.

3.1.2 Movement of International Investment

Another closely related factor is the movement of investments in and out of the Canadian economy. Every day companies, financial institutions, and individuals make investments around the world, be it purchasing foreign stocks and bonds, buying foreign exports, or engaging in business activities in another country. Changes in the flow of these investments between Canada and other countries can, in turn, impact the value of the Canadian dollar.

A similar process occurs whenever any foreign investor makes an investment in Canada, be it the buying of stocks or bonds, making a business investment, or purchasing Canadian exports. In order to make these investments in Canada, the foreign investor must first acquire the necessary Canadian dollars in the international currency markets. Growth in the level of foreign investments, therefore, results in increased demand for the Canadian dollar. If the supply of the dollar is not adjusted accordingly, then its price may also rise in value relative to other currencies.

An opposite effect can occur whenever investments leave the country. This happens when there is a downturn in foreign purchases of Canadian stocks, bonds, businesses or exports, or when there is growth in Canadian investments in other parts of the world. This causes lower demand for the Canadian dollar and an increase in its supply, resulting in a lower price unless the currency supply is adjusted accordingly.

3.1.3 Speculative Trading & the Canadian Dollar

Just as in stock markets, there is also a high level of speculative activity in international currency markets. Many investors trade national currencies — not because they need them to make actual business investments, but because they looking to make profits on changes in the value of currencies over time. These investors will buy large amounts of a currency on the speculation that it will increase in value over time, and that they will be able to sell the currency for a profit at a later date.

These speculative activities can impact the price of the Canadian dollar relative to other currencies. When speculative investors believe the price of the Canadian currency will increase over time, they will change their holdings from other currencies to the Canadian dollar. This, in turn, increases demand for the Canadian dollar and will consequently increase its price relative to other currencies, if the supply is not adjusted accordingly. Similarly, if speculative investors believe the dollar is weak and will lose value over time, then demand will fall and supply will rise as investors sell off their investments. This, in turn, can result in a sharper decrease in the price of the Canadian dollar relative to other currencies.

3.2 Bank of Canada and Monetary Policy

The Bank of Canada observes and analyzes domestic and international economic/financial trends and highlights important national goals. Moreover, it has the authority to manipulate important financial levers, such as the money supply and interest rates, in order to achieve these goals and objectives. As such, the Bank of Canada plays a significant role in the economic and financial life of the country, and has a great influence on the value of the Canadian dollar.

3.2.1 Regulating the Money Supply

How exactly does the Bank of Canada influence the price of the Canadian dollar? One way is through direct manipulation of the money supply in currency exchange markets. The Bank of Canada accomplishes this by buying and selling Canadian currency in the market in order to adjust the supply of dollars available for investors and speculators.

Take, for example, a situation in which market investors and speculators are selling off their holdings of Canadian dollars in large quantities. Such a situation could lead to a drastic fall in the price of the Canadian dollar, as demand weakens and a flood of Canadian dollars hit the market. In order to moderate this change in price, the Bank of Canada will intervene by using its foreign currency reserves to buy massive quantities of Canadian dollars. This, in turn, reduces the supply available and should stabilize the dollar’s price.

It is important to note that, in some cases, individual governments and central banks simply do not have the financial reserves necessary to cope with drastic fluctuations in the value of their currencies. As a result, central banks will often work closely with one another when such interventions become necessary. This may include lending money to one another, or coordinating interventions in the currency markets in order to stabilize a vulnerable currency.

3.2.2 Manipulating Interest Rates

Another important factor is the level of interest rates in Canada. Interest rates constitute the amount lenders charge individuals and businesses to borrow money. Suppose the interest rate in Canada is higher than in the United States (particularly after each country’s rate of inflation is taken into account). This means that lenders can get a higher rate of return for lending in Canada than in the United States. In order to take advantage of this higher rate of return, international investors will shift their portfolios (for example, government bonds) from the United States to Canada.

These sorts of shifts cause an increase in demand for Canadian dollars. In order to buy Canadian government bonds, investors first have to purchase Canadian dollars; the result is an increase in the demand for Canadian currency. Meanwhile, the demand for the US currency would fall as investors divest themselves of US government bonds in order to reinvest that money in Canada, where they can gain a higher rate of return. The overall result: a rise in the value of the Canadian currency relative to its US counterpart.

As such, the Bank of Canada can attempt to influence Canadian dollar exchange rates by manipulating the interest rates. If the Bank wishes to stop or slow a drop in the value of the Canadian dollar, it may raise interest rates to levels higher than in other nations; this, in turn can spur investment in Canada relative to other nations and demand for the dollar. Conversely, if the Bank wishes to stop or slow a rise in the value of the dollar, it can do so by lowering interest rates below other countries, thus causing lower relative investment and demand for the dollar.

It is, however, important to note that manipulation of interest rates for monetary policy is a very complex task. For example, while higher interest rates may spur higher demand for the Canadian dollar amongst lenders, it can also reduce demand amongst other economic actors. As explained earlier, the value of the dollar depends in large part on the level of business activity and foreign investment. High domestic interest rates often have the result of slowing down general economic activity and investment, as businesses and consumers cannot cheaply borrow the money they need to continue or expand their operations or make consumer purchases. This economic slowdown can, in turn, reduce domestic and international demand for Canadian dollars.

3.2.3 Controlling Inflation Rates

Another important tool in monetary policy is controlling inflation rates. Inflation is the rate at which prices for goods and services rise over time. For example, in the 1950s, a bottle of soda pop cost Canadians a dime, while today that same bottle costs nearly two dollars. This increase in price over time (inflation) represents a long-term erosion of the purchasing power of the Canadian dollar; whereas one Canadian dollar used to be able to purchase 10 bottles of pop, now it can only purchase half a bottle.

While every modern economy experiences a certain level of inflation, businesses and investors generally prefer an economy with low and stable levels of inflation. Not only does this protect their investments from eroding substantially in value, it also allows for long-term business planning and investing. With low and stable levels of inflation, businesses can predict what their production costs (for equipment, technology, and labour) will be over the long-term. This, in turn, makes those investments safer and encourages companies and individuals to do business in the economy.

It is at this point that we can see the importance of inflation and the value of the Canadian dollar. If inflation in Canada is higher than in other countries, domestic and foreign investors will prefer to do business in other nations. This, in turn, causes lower demand for the Canadian dollar and a downward pressure on its value in international currency markets. The exact opposite is true if inflation in Canada is low relative to other countries; low inflation will spur the flow of investment dollars into Canada, increase demand for the Canadian dollar, and place an upward pressure on its value.

In order to control inflation, the Bank of Canada actively pursues inflation targets, and does so by manipulating interest rates (or the cost of borrowing) and consumers' spending habits. Take, for example, a situation in which inflation is rising at high levels (meaning that prices for goods and services are increasing substantially each year). To combat such increases, the Bank of Canada will raise interest rates. These higher rates will lead to lower consumer demand in the economy, as it becomes much more expensive to borrow in order to purchase goods and services. Lower consumer demand should, in turn, cause prices to stabilize over time, thus bringing inflation under control.

The housing market is a useful illustration of this. Higher interest rates mean that home mortgages become more expensive. This leads to lower demand in the housing market, as many buyers cannot afford the higher mortgage payments. With fewer home buyers, the housing market usually ‘cools down,’ meaning that home prices stabilize or even fall.

3.2.4 Ensuring Political Stability

While not a part of monetary policy, another important method of influencing the value of the Canadian dollar is by ensuring political stability. Investors generally prefer economies that are very stable politically, as this allows for long-term business planning and investing. If a nation becomes politically unstable, domestic and international businesses tend to become more cautious in their investments. This, in turn, can reduce demand for Canadian dollars and lower its value in international currency markets.

3.3 Changes in the Value of the Canadian Dollar: Consequences

3.3.1 International Trade & the Economy

Almost every country in the world engages in trade with one another; countries import goods and services from other nations, as well as export their own domestic products. Exchange rates have an important role in this process. When Canadians import goods and services from the United States, for example, they usually do so in American currency. Canadian importers must first exchange their Canadian dollars for American funds, and then use those funds to buy American products. The same is also true with regard to Canadian exports: when buying Canadian goods and services, foreign consumers must first exchange their currencies for Canadian dollars.

Changes in exchange rates, therefore, can causes changes in the price of Canada’s imports and exports. If, for example, Canada’s currency significantly increases in value relative to the currencies of its trading partners, then importing foreign goods and services becomes much cheaper. Canadians gets a bigger "bang for their buck" when exchanging their Canadian dollars and purchasing foreign products. At the same time, however, Canadian exports also become more expensive for other countries to purchase, as foreign importers must exchange more of their currencies in order to buy Canadian products. The exact opposite effect can occur when Canada’s currency drops significantly in value relative to its trading partners. Foreign imports become more expensive, while the nation’s exports become cheaper for other nations to buy.

These changes in exchange rates and import/export costs can have significant consequences for Canada’s economy. When the Canadian dollar rises in value, Canadian producers are often faced with stiffer foreign competition at home, as the cost of foreign imports becomes cheaper. A higher Canadian dollar also means Canadian exporters must deal with higher prices for their products abroad, with the possibility that foreign consumers may look elsewhere for cheaper prices. There are, however, some benefits to a higher Canadian dollar. Many Canadian producers depend on foreign imports when producing their goods or services (such as raw materials, machinery, or technology). A higher Canadian dollar means lower production costs and greater competitiveness for these Canadian producers.

Again, the exact opposite effect can occur when the Canadian dollar drops in value. A lower Canadian dollar means less competition for Canadian producers at home, as foreign imports come more expensive for Canadians to purchase. Canadian producers that depend on foreign imports when producing their goods and services, however, face higher production costs. Finally, Canadian exporters gain a price advantage internationally, as their products become cheaper for foreign consumers to purchase.

It is important to note, however, that recent improvements in technology and international transportation have made it possible for modern economies, including Canada’s, to reduce the risks of currency fluctuations. Many North American companies, for example, have developed networks of domestic and international suppliers for many components of their products, or stages of their production processes. Factors such as the rising "import content" of Canadian exports and "just-in-time" inventory management systems have allowed many Canadian producers to withstand the drastic increase in value of the Canadian currency relative to the US dollar that took place in the late 1990s and early 2000s — something that might have put them out of business in an earlier era.

3.3.2 International Trade & the Cost of Living

The relationship between exchange rates and international trade impacts not only Canadian producers, but also Canadian consumers; in particular, the cost of living for consumers (or the average cost of basic goods and services, such as food, shelter, and clothing). Canadians today depend on many foreign imports for their basic needs, be it agricultural products, building supplies, manufactured garments, and so forth. Changes in Canadian exchange rates can make these foreign goods and services more or less expensive to import, which, in turn, influences how much Canadians must pay to cover their basic needs.

For example, during the winter months, Canadians usually depend on fruits and vegetables imported from the southern United States. If the Canadian dollar decreases in value relative to the US dollar, then Canadians are forced to pay more in their domestic currency to purchase these basic goods imported from the US. As a result, the daily food cost for Canadians rises and they experience an upward pressure on their cost of living.

These sorts of changes can have important social impacts, especially for low-income or fixed-income earners. Drastic increases in the cost of living means that persons have less purchasing power to pay for imported goods and services they depend upon. For those close to the poverty level, this can have dire consequences. Conversely, a rise in the value of the Canadian dollar means cheaper foreign imports, and a decrease in the cost of living. As a result, persons have a greater financial capacity to buy their basic goods and services.

3.3.3 Exchange Rates & Foreign Debt

Exchange rates also can have an important impact on government finances. Canadian territorial, provincial and federal governments, like most governments in the world, have some level of foreign debt — that is, debt they owe to foreign financial institutions or governments. In many cases, this foreign debt is held in a foreign currency (be it that of the lender or of a major foreign currency, such as the United States or the European Union’s). As such, changes in exchange rates can have considerable implications for the costs associated with maintaining and paying back this foreign debt.

In this context, let’s look at another example. Say, for instance, the Canadian federal government borrows $1 billion in American currency from a US bank when the Canadian dollar is valued at US $0.90 (meaning one Canadian dollar is worth 0.90 American dollars, or 90 cents). The cost of paying back that loan (without interest) would be around $1.1 billion in Canadian currency. If, however, the value of the Canadian dollar was to drop to US $0.62 (so that one Canadian dollar equaled only 62 American cents), then the cost of paying back that same loan in Canadian currency would climb to CAN $1.6 billion, an increase of $500 million Canadian dollars. The exact opposite holds true when the dollar increases; loans taken out at a lower exchange rate become much cheaper to maintain and pay back as the currency value rises in relation to the lender’s currency.

These sorts of changes can have further political and social impacts. If the value of a nation’s currency were to fall, and the cost of maintaining loans (held in foreign currency) were to rise substantially, then governments must find ways to compensate. This may mean increasing taxes, reducing social spending, or running a deficit. The opposite is true if the currency rises; with lower loan costs, additional funds are available for cutting taxes or investing in social programs.

CHAPTER 4 ECONOMETRIC METHODOLOGY

In this chapter explains basic terms of econometric methodology, which includes mathematics, statistical methods and computer science.

BEER_Eur-USD (p. 47)

4.1 Time series and stochastic processes

A time series is a sequence of data points representing the movement of variable at uniform time interval. Referring to series of observations as a time series, some regularity of observation frequency is assumed, in the case of this study – it is monthly data. A stochastic process is a sequence of random discreet variables belonging to a domain R which represents a common probabilistic space that all joined probabilities exist. If is defined as a stochastic process, will denote the realization of discreet-time stochastic process, which is finite R. time series analysis is used to address a number of economic issues in the reality, valid for many different macroeconomic estimations and forecasts. The general idea is to explain the possible relationship in a generated model between some presumably related variables, or ideally to uncover any cointegration in an economic system (Lutkepohl, 2006).

A stochastic process is said to be stationary if its means and variance are constant over time and the value of the covariance between two periods depends only on the distance between the two time periods and not on the actual time, at which the covariance is computed (Gujarti, 2004, p. 797). It represents a "basic model" of time series analysis, characterized by a zero mean and constant variance.

Mean: E()=μ=0,

Variance: var()=E(- μ=σ²<∞,

Covariance: cov=E[(- μ)(- μ)]

and since μ=0, the equation can be re-written:

E(

Such stationary time series will tend to return their mean (also called mean reversion). The fluctuations around this mean have constant amplitude. The time series data would not be scattered in a different uncorrelated episodes, but will represent a whole process. This is very important as it has particular practical value for forecasting processes.

A stochastic process is called a random walk or white noise when its first differences have a zero mean, constant variance and are serially uncorrelated.

σ²;

The term "random walk" was first introduced by Karl Pearson in 1905 and is often described as a "drunkard’s walk" (Dixon, 2004), i.e. randomly taken steps constituting developed trajectory.

4.2 Test for normality

Jarque-Bera test for normality

The multicollinearity problem occurs when two or more regressors are highly correlated in a multiple regression.

Jarque-Bera (JB) test for normality analyzes whether the residuals from regressions are normally distributed, since this is one of the properties of OLS estimators under the normality assumption (Brooks, 2002). In order to make conclusions on coefficients' truthfulness and the estimated model, the residuals are required to follow a standard normal distribution. The test computes the skewness and kurtosis of the OLS residuals. Kurtosis is a measure of peakedness with less density in the middle, whereas the skewness is associated with the fat-tails of a normal distribution. The latter has ideally a kurtosis of 3.0 and skewness of 0. Therefore, the joint hypothesis, where the JB statistic is expected to be 0, so Ho: S=0 and K=3. In other words, the Ho tests whether the residuals are normally distributed. It follows a Chi-square with 2 degrees of freedom distribution (Brooks, 2002). If the computed JB statistic is smaller, that indicates that the residuals are normal.

4.3 Regression analysis

Regression analysis is almost certainly the most important tool at the econometrician’s disposal. But what is regression analysis? In very general terms, regression is concerned with describing and evaluating the relationship between a given variable and one or more other variables. More specifically, regression is an attempt to explain movements in a variable by reference to movements in one or more other variables. To make this more concrete, denote the variable whose movements the regression seeks to explain by y and the variables which are used to explain those variations by x1, x2, . . . , xk . Hence, in this relatively simple setup, it would be said that variations in k variables (the xs) cause changes in some other variable, y.

4.3.1 Ordinary least Squares (OLS)

The method of ordinary least squares is attributed to Carl Friedrich Gauss, a German mathematician. Under certain assumptions the method of least squares has some very attractive statistical properties that have made it one of the most powerful and popular methods of regression analysis. For understanding this method the least squared principle was explained. For this equation for two-variable population regression function (PRF) [2] was taken:

However, the PRF could not be observed directly, therefore, we estimate it from sample regression function (SRF) [3] :

(!!!)

where is the estimated value of .

First of all, for determination SRF equation (!!!) would be rewritten as

(@@)

Equation (@@) shows that is simply the differences between the actual and estimated Y values. After given n numbers of observations on Y and X, the SRF would be determining in such manner that it is as close as possible to the actual Y. And in the end, necessary to choose the SRF in such way that the residuals’ sum ∑=∑ ( is as small as possible (criterion of minimizing). The hypothetical scattergram below expresses this criterion.

Figure *** Least squares criterion

C:\Users\Shmel\Desktop\2.bmp

Figure (***) shows that the residuals and the same as and receive the same weight in the sum (), whereas the first two residuals are much closer to the SRF that the next two. In other words, all residuals receive equal importance no matter the distance from the SRF. Consequences of this is the possibility that the algebraic sum of the could be small, even zero. Assume that values of are 10, -2, +2, and -10, respectively; in this case the algebraic sum equal zero. This problem could be avoided through the adaptation least squares criterion, which states that the SRF can be fixed in the way that is the sum of squared residuals is as small as possible:

∑

∑

In this situation residuals such as and have more weight than the residuals (Figure ***). In comparison with minimum ∑ criterion, where the sum can be smaller even through the , under the least squares procedure for larger (in absolute value), the large ∑.

4.4 Autoregressive conditionally heteroscedastic (ARCH) model

Autoregressive conditionally heteroscedastic (ARCH) model is widespread usage in finance. Typical structural model could be expressed by the follow equation:

And in additional was assumed that . The assumption of the classical linear regression model (CLRM) is that the variance of the errors is constant is called homoscedasticity. In the opposite, if the variance of the error is not constant, this is would be known as heteroscedasticity. To understand how the ARCH model works, it is necessary define what is conditional variance of a random variable, . The difference between the conditional and unconditional variances of random variable is the same as that of the conditional and unconditional mean. The conditional variance of may be denoted , which is written as follow:

It is usually assumed that E()=0, so

(#)

Equation (#) states that the conditional variance of zero mean normally distributed random variance is equal to conditional expected value of the square of . Under the ARCH model, the ‘autocorrelation in volatility’ is modeled by allowing the conditional variance of the error term, , to depend on the immediately previous value of the squared error:

The above model is known as an ARCH(1), since the conditional variance depends on only one lagged squared error. Notice that (8.10) is only a partial model, since nothing has been said yet about the conditional mean. Under ARCH, the conditional mean equation (which describes how the dependent variable,, varies over time) could take almost any form that the researcher wishes. One example of a full model would be:

The model given by (8.11) and (8.12) could easily be extended to the general case where the error variance depends on q lags of squared errors, which would be known as an ARCH(q) model:

The testing for ‘ARCH effects’ consist in statement that all q lags of the squared residuals have coefficient values that are not significantly different from zero. Null hypothesis are rejected if the value of the test statistic is greater than the critical value from the distribution. The test can also be thought of as a test for autocorrelation in the squared residuals. As well as testing the residuals of an estimated model, the ARCH test is frequently applied to raw returns data.

4.5 Generalized ARCH (GARCH) model

The GARCH model was developed independently by Bollerslev (1986) and Taylor (1986). The GARCH model allows the conditional variance to be dependent upon previous own lags, so that the conditional variance equation in the simplest case can be written as

This is the GARCH(1,1) model. is known as the conditional variance since it is a one-period ahead estimate for the variance calculated based on any past information thought relevant. Using the GARCH model it is possible to interpret the current fitted variance, , as a weighted function of a long-term average value (dependent on ), information about volatility during the previous period () and the fitted variance from the model during the previous period ().

CHAPTER 5 ESTIMATION RESULTS

5.1 DATA

All time-series, used for performing this econometric study, are in monthly frequencies for the period 1995:1 – 2012:8. The time frame consists of 212 observations. The estimates are made with statistical program Gretl. The variables such as price ratio and exchange rate are examined in logarithms; money market rate and short-term interest rate differentials as they are in percentages.

The nominal exchange rate is quoted as USD/CAD with the USD as normalized to 1, i.e. the time-series represent the movements of the CAD relative to the value of 1 USD. The data is extracted from OECD.Stat.

The money market rate series are obtained from IMF.

The short-term interest rate for both countries is obtained from OECD.Stat.

The price ratio are taken as ratio of US CPI towards Canada CPI with a base year 2005 (=100). Data are extracted from CEIC.

4.2 Testing for unit roots

Testing for stationarity of time-series is the initial procedure when performing an econometric analysis. Many financial and economic time series exhibit trending behavior or nonstationarity in the mean. An important econometric task is determining the most appropriate form of the trend in data. Unit root tests can be used to determine if trending data should be first differenced or regressed on deterministic functions of time to render the data stationary. The augmented Dickey-Fuller (ADF) test is used to test for the stationarity of our data. The null hypothesis of this test is that time series has a unit root and is not stationary. If we reject this hypothesis then we conclude that the series is stationary. On the other hand, to not reject the null means that the level is not stationary. For rejecting it necessary that p-value was less than 5% or 0.05.

Gretl expresses the model as following:

The coefficient is included because we believe the series has a trend, is the coefficient of interest in the Dickey-Fuller regression, and is the term that ‘augments’ the Dickey-Fuller regression. It is included to eliminate autocorrelation in the model’s errors,, and more lags can be included if needed to accomplish this.

ADF test on stationary: (Appendix Fig. 1, 3 ,4, 5)

Variable

Lags

Asymptotic p-value

I(d)

ExRate

1

0.3331

Not 0

MMR

9

0.01205

I(0)

I

10

0.00195

I(0)

PriceRatio

12

0.4732

Not 0

The table summarizes the results from ADF tests. The results suggest that the money market rate and short-term interest rate differentials are integrated of order 0, that is they are stationary, because their p-value is lower than 0.05. On the other hand, the exchange rate and price ratio are nonstationary. This means that they exhibit trend behavior and will be differentiated further until stationarity is reached. Thus, the first differences of those variables are obtained.

ADF test on first differences of variable: (Appendix Fig. 2, 6)

Variable

Lags

Asymptotic p-value

I(d)

D(ExRate)

3

0.00075

I(1)

D(PriceRatio)

11

0.0046

I(1)

The ADF test results show that there are no more unit roots in the data as the Ho is rejected. This implies that the log levels on these variables are integrated of first order, because after differentiating ones the log level became stationary.

Normality test

OLS Regression

Ordinary least-squares (OLS) regression is generalized linear modeling technique that could be used to model a single response variable which has been recorded on at least an interval scale. The technique may be applied to single or multiply explanatory variables and also categorical explanatory variables that have been appropriately coded. In basic, with the help of OLS regression, relationship between a continuous response variable (Y) and a continuous explanatory variable (X) could be estimate. Linear relationships represented by mathematically equation which describe straight line Y=α+βx, where α indicating the value of Y when X is equal to zero (known as intercept) and β indicating the slope of the line (known as the regression coefficient) (Hutcheson, G. D. 2011).

(Appendix Fig. 7)

p-value

R-squared

Durbin-Watson

Const

Constant

0.9827

0.989

1.962

MMR(-1)

Money market rate differential

9.36e-05

I

Short-term interest rate differential

2.15e-05

PriceRario

Log of price ratio

0.4563

Ln[y1(-1)]

Log of exchange rate

4.35e-046

Ln[y2(-2)]

Log of exchange rate

0.0005

The table summarizes the results getting from OLS linear regression. The Durbin-Watson test’s result around 2 what indicates no autocorrelation. R-squared near 1 indicates that a regression line fits the data well. P-value shows level of significance; we can suggest that money market rate and short-term interest rate appear to be significantly related to exchange rate.

Test for ARCH

ARCH models are used to characterize and model observed time series. The null hypothesis is following: no ARCH effect is present. Test for ARCH shows that Chi-square(12) is equal 24.9382 what is greater than critical value (21.0261). This means that we reject null hypothesis as ARCH effect is present. Thus, test for GARCH should be done. (Appendix Fig. 8)

Test for GARCH

(Appendix Fig. 13)

Model 3: GARCH, using observations 1995:03-2012:08 (T = 210)

Dependent variable: ExRate

Standard errors based on Hessian

Coefficient

Std. Error

z

p-value

const

-0.000970693

0.00265168

-0.3661

0.71432

MMR_1

0.00908723

0.00418338

2.1722

0.02984

**

I

-0.0107162

0.0042782

-2.5048

0.01225

**

PriceRatio

-0.0109204

0.0696352

-0.1568

0.87538

ExRate_1

1.2527

0.0742698

16.8668

<0.00001

***

ExRate_2

-0.253265

0.0753487

-3.3612

0.00078

***

alpha(0)

2.06226e-05

1.92347e-05

1.0722

0.28365

alpha(1)

0.126649

0.0923275

1.3717

0.17015

beta(1)

0.803381

0.140861

5.7034

<0.00001

***

Mean dependent var

0.238159

S.D. dependent var

0.158381

Log-likelihood

572.4910

Akaike criterion

-1124.982

Schwarz criterion

-1091.511

Hannan-Quinn

-1111.451

Unconditional error variance = 0.000294736

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