Canadian Exchange Rate Essay, Research Paper

Introduction

The Canadian Dollar has undergone a significant depreciation over the past 10 years. The drop in relative value of our currency has caused a great deal of consternation not only among economists but also in the media and consequently the general public has well. Ordinary citizens experience first hand the effects of such depreciation every time they go to our most frequented vacation spot, the United States. While economic variables are not usually the subject of casual debate, the exchange rate trend has even permeated our most beloved conversation topic, professional hockey. Despite the popularity of the subject, consensus and clarity are rarities. What has happened to the value of the Canadian dollar simply requires quick glance at the data, however why it has happened is rather more contentious. This paper will analyze the long term effect of the Canadian exchange rate relative to the US dollar. The first section will serve as a background piece on exchange rates. In the next section, I hope to provide the reader with an appreciation of what has happened to the value of the Canadian dollar over the last decade. In the third part I will go through the economic theory behind the determination of a long term exchange rate. Finally in the fourth section, I will try to relate the theory with the trend exibited by the Canadian dollar.

Section 1 Background

While the subject is often discussed, there still exists many misconceptions about what the exchange rate actually is. The exchange rate is the price of a foreign currency in Canadian dollars on the foreign exchange market. Like in any market, the price is determined by the intersections of demand and supply. Demand for a currency is made up of all those who want to buy or hold an asset in that particular currency. For example, importers need to convert the Canadian dollars into foreign currency in order to purchase foreign goods. Similarly investors who wish to hold foreign assets must pay for them in foreign currency and therefore need to convert Canadian dollars. The supply is made up of those wishing to buy Canadian dollars; these people include those buying Canadian export and those investing in Canadian assets. The intersection of theses two opposing actions, buying and selling Canadian dollars determines the volume traded and at what price or the exchange rate. Due to geographic proximity, free trade and economic integration, the foreign currency most demanded and most sold by Canadians is the US dollar. The value of our currency is most reflected in the price of the US dollar. This paper will therefore use the price of a US dollar in terms of Canadian dollars as the value of the Canadian dollar.

In the previous section I assumed that the currency is flexible, that is to say that the price is based on foreign exchange market activity. It is however possible to fix the price of a currency at a particular level. In order to accomplish this, the central bank must be willing to buy or sell the perceived excesses of the market; i.e. the bank must buy or sell enough Canadian dollars so that the price remains stable. If such a practice becomes unsustainable the central must change the fixed price or move the peg. Such a system, known as the Breton Woods system was predominant in post-world war II industrialized economies. However by the Nineteen sixties Canada, Canada like many other nations, moved to a flexible exchange rate system. It is important not to assume that because the currency is not officially fixed at some level, that the central bank does not play a role in determining its price. The central bank still intervenes in the market but not to hold the price at a certain level, but rather to prevent to price from fluctuating rapidly up or down. This type of exchange rate regime is known as a dirty float.

Section 2 Observations

Over this past decade, the value of a Canadian dollar has dropped nearly 25%. In 1990, a US dollar could be purchased for 85 cents Canadian and by the end of 2000 the price had dropped to 65 cents. This decline however, has not been constant. Between 1990 and the end of 1991, before the recession, the dollar actually appreciated to three cents. The end of ninety-one marked the beginning of a steep depreciation of the dollar. In fact notwithstanding a few blips, the price of a dollar only leveled out in 1995 but not before sinking to 71 cents. This equilibrium did not last very long; by the beginning 1997, the dollar was sliding again only to stop two years later at around 65 cents. This all-time low was most likely considered unsustainable and the price slowly crept its way back towards the 70-cent level throughout 1999 only to drop back down to 65 cents by the end of 2000.

That Canadian dollar over the 1990’s has steadily declined 25%, cannot be simply what is known as a market error. The invisible hand of Adam Smith has not been waving around the foreign exchange and accidentally knocking down the Canadian dollar. A steady long term trend downward.

ds means that economic fundamentals are at play.

The question of what economic fundamentals have forced the depreciation of the Canadian dollar is indeed a sordid one. Over the years economists have developed several theories regarding the determinants of exchange rates. However because the downfall of the Canadian dollar seems to be a long-term trend I will disregard the short-term determinant known as the interest rate parity. The interest rate parity hypothesis claims that because most foreign exchange transactions involve financial asset, which have no sunk costs and are readily convertible. Therefore in the short term arbitrage accounts for most of the fluctuations in the exchange rate. This implies that the forward exchange rate should be an unbiased estimate of the future spot rate. Unfortunately this is generally not the case in a simple model (see appendix) but still economist believe it to be true (Isard p 89).

Section 3: The PPP Theory

Although a relationship between the exchange rate and price levels was suspected as early as the 1600’s (Isard p57), it was not until 1918 that this link became known as the purchasing power parity or PPP. Essentially PPP rests on the notion that people pay one price for goods, so that a good in one country will be as cost the same as it does in another country. If there was a difference in price between the two countries, people would simply buy the good in the “cheaper” country and bring it back home where they could sell it and thereby forcing the price in their home country down until the prices in both country are the same. This practice is known as arbitrage. From these assumptions we can extrapolate that the exchange rate must be equal to the ratio of price levels of the two countries:

Where S is the exchange rate and P is the domestic price level and P* the foreign price level.

Unfortunately such a proposition is impossible to evaluate. The price levels are difficulty quantifiable. Think of it as asking someone to determine how much he or she enjoys a movie. Clearly one cannot simply say “oh it was about 6″ and expect the questioner to understands what the answer means. The way to properly answer the question is to provide a frame of reference for your answer, for example saying “it was a 6 out of 10.” Even then your criteria for a 6 could be much different then someone else. The same rational applies to price levels. In order to compare two price levels it is necessary to view price levels as the cost of a basket of the goods. However it is also necessary for those baskets to contain exactly the same goods. Moreover, the goods must also be tradable; the PPP works only if arbitrage is allowed to occur. Therefore when testing PPP we must use price indices which trace the cost of a basket of goods over a number of years relative to a base year. Thus, we are actually taking the ratio of the rates of change in the price level. This derivation of the PPP is called the Relative Purchasing Power Parity:

Where S is the exchange rate and P is the domestic price level, P* the foreign price level and r is a constant parameter known as the real exchange rate.

The real exchange rate being constant is a fundamental tenet of the PPP hypothesis and is quite easy to evaluate. In order to do so I must first collect the necessary data. Statistics Canada offers a rather extensive collection of data sets through its CANSIM database. There, I collected the consumer price indices for Canada and the US as well as the spot exchange rate. Then, I logged the variables so that I can test, using an ordinary least squares estimation method, the value of a, b1 and b2 in the equation:

Where s, p and p* are the respective logs of the exchange rate, the domestic price level, and the foreign price level.

For the Relative Purchasing Power Parity hypothesis to hold I must find that b1=b2=1. In order to test this I execute an F-test with two restrictions, b1=1 and b2=1.

That the Relative Purchasing Power hypothesis does not hold is no surprise. In fact it would have been surprising to find that it was true. There are two types are reasons for this, one relating to the inadequacy of my test, and the other to the validity of hypothesis in general.

The test I executed was inherently flawed since I used consumer price indices that are not necessarily the same as general price indices. CPIs only reflect the prices that typical consumers pay, this excludes the prices of high volume goods such as manufacturing inputs that may be more responsive to the exchange rates. Moreover, my sample size is small, only 42 data points, as well as being spread over a relatively short period of time, ten years. However more elaborate models of relative PPP were found that the real exchange rate tends exhibit mean reversion in the long term.(Isard p65) In other words, that the deviations from the expected real exchange rates tend to be normally distributed. However, this is not the same thing as saying that the real exchange rate is constant since it does vary with time. Which leads us to why the PPP hypothesis is difficult to substantiate even in the long run. Unfortunately for those who study them, economies are not static entity. Rather they grow, shrink and re-tool over time. For the real exchange rate to be constant and thus for PPP to hold, nothing but money stocks and the price levels can change. (Fritz). Since this is an extremely unrealistic proposition, some economist claim that the PPP may be right in theory but hardly descriptive of what actually happens in practice. Going even further, Fritz Machlup writes, “[t]he survival of the purchasing power parity theory in present-day discussions among international monetary economists is a sorry reflection of their critical judgement.” However being a resilient bunch, academics have reassessed their models of PPP in an attempt to adjust the real exchange rate for factors that contribute to structural change in an economy. For example one could discount the variability in the real exchange rate using the Balassa-Samuelson effect which states that the real exchange rate will shift as a result of the differences in relative productivity of the traded goods sector(faria). In essence though these models serve only to test PPP for traded goods as opposed to PPP as a whole (Isard p66). Moreover, recent empirical result have not supported the Balassa-Samuelson effect, likely because in the long run, productivity differentials disappear due the dissemination of knowledge and the mobility of human and physical capital. Although this could strengthen the argument for PPP the same study also found that the real exchanges rates impacts the relative growth rates, which means that the real exchange rate is not neutral, which implies that PPP is false.

Section 4: Analysis

Nevertheless, it is unlikely that on some level PPP does not hold. The law of one price is fundamental to economic theory. Moreover, the Free Trade Agreement signed at the outset of the nineties means that the complete or perfect arbitrage is even more likely. It is therefore reasonable to assume that the differences in price levels push the exchange rate in a particular direction. In addition to the PPP factor, there is also the effect of interest rate differentials, which one would expect to be irrelevant over ten years unless there is a bubble factor which also would affect the exchange rate’s direction. Finally, irrationality in the foreign exchange market could also serve to push the exchange rate one way or another. I would argue that the decline in the value of the Canadian dollar is a combination of these three factors.

For the real exchange rate to have remained stable while the nominal rate depreciated 25% means that there must have been a change in the relative price level. However, as illustrated in the previous sections, the price levels have remained more or less constant. However, you will recall that in that case we used the CPI as a measure of price levels. What the CPI fails to incorporate however is the degree to which certain prices such as commodity prices are important to the overall economy. The point is that when comparing CPIs, we are unable to discern the fact Canada’s economy relies relatively more on commodities than the US does, which is in fact the case. Thus, a drop in commodity prices might not affect the CPI but would effect the true price level. In fact in a recent paper by John Crow, affirms that commodity prices fell about 20% over the last ten years, which is about what the exchange rate fell by. Thus Canadian commodity producers were made “made whole.” In addition to price level adjustment, structural change may also be also have an impact on the exchange rate. Djoudad and Tessier find that the dept to GDP ratio explains 20% of the variability in the exchange rate. The debt to GDP ratio helps to explain the drop in the early nineties but becomes irrelevant later on in the decade as the ratio decreased yet the dollar continued its slide. Because of this one way impact, I am tempted to associate the debt to GDP ratio not in the structural change argument but rather with irrationality in the foreign exchange market. Paul Krugman puts forth another reason why PPP may not fully explain the change in the exchange rate. Krugman hypothesizes that foreign investors incur sunk costs as soon as they invest in a foreign market. The investor, realizing that exchange rates are variable in the short run, will hold off selling his foreign assets until he or she is sure that the value of the currency has indeed experienced a real depreciation. Such a hypothesis could explain the slow and continued trend downward of the Canadian dollar.

The growth in the US over the past has been astonishing. As someone who was born after 1973, it is difficult for me to imagine a sustainable growth rate upwards of 5%. Nonetheless, the data slowly trickling in seems to indicate that US productivity levels have kept up with the income growth thereby rendering it sustainable. It appears that the penny-pinching business practices forced upon firms during the recession of the early nineties as well as the increased use of computers have cleared the way for a new era of economic growth. Despite this advent, the value of the stock market still seems out of control:

I realize that the interest rate parity hypothesis should mean that the exchange rate has already incorporated these high returns, as the interest rate is the opportunity cost of money. However because the interest rates in the two countries have tracked each other over the past decade, it is my supposition that this “bubble” in the US stock market has not been fully incorporated into the interest rate. This seems logical since the man who controls US interest rates has been quoted as saying the growth of in equity markets is the result of “irrational exuberance.” With the interest rate in the US not being reflective of the expected return on capital it is possible that capital outflows are another factor pushing the exchange rate down. In addition to Canadian dollars being sold, such a situation would be further reinforced by the capital outflows from all other countries, which would push up the value of the US dollar. Although I have no direct evidence to support such a contention, it is a possibility worth exploring in the future.

Another facet of irrationality and the exchange market is the behavior exhibited by investors who are not risk consistent. That is to say that investor have a tendency to alter their risk preference once the have lost a significant amount of money. The past decade has certainly not been lacking in its share of currency crises: Mexico in 1994, the Asian crisis in 1998, and the poor performance of the Euro. This may have caused investors to view the US dollar as the only safe heaven. If this is correct, then in true circular fashion the US dollar would appreciate against all other currency, which its seems to have done according to the chart below especially after 1996.

Crow, John. “Canadian Exchange Rate Policy”; Canadian Public Policy, Vol. XXV, no3. 1999.

Djoudad R. and Tessier D. “Quelques r?sultats empiriques relatifs ? l’?volution du taux de change Canada/?tats-Unis,” Bank of Canada, Working Paper 2000-4. 2000.

Faria, Joao and Leon-Ledesma, Miguel. “Testing the Balassa-Samuelson Effect: Implication for growth,” University of Kent at Canterbury, Department of Economics Discussion Paper 00/08. 2000.

Isard, Peter. Exchange rate Economics; Cambridge University Press, 1995.

Krugman, Paul. Exchange rate instability; The MIT Press, Cambridge USA. 1989.

Machlup, Fritz. Explainig Changes in Balances of Payments and Foreign Exchange Rate: a Polemic without graphs, Algebra, and Citations. Flexible Exchange rates and the Balance of Payments; Chipman and Kindleberger editors, 1980. p99.

James Powell A History of the Canadian Dollar

http://www.bankofcanada.ca/en/dollar_book/index.htm