IN
DEGREE PROJECT TECHNOLOGY, FIRST CYCLE, 15 CREDITS
STOCKHOLM SWEDEN 2017,
Understanding and Exploiting commodity currencies
A Study using time series Regression DYLAN DEHOKY
EDWARD SIKORSKI
Understanding and Exploiting commodity currencies
A Study using time series Regression DYLAN DEHOKY
EDWARD SIKORSKI
Degree Projects in Applied Mathematics and Industrial Economics Degree Programme in Industrial Engineering and Management KTH Royal Institute of Technology year 2017
Supervisors at KTH: Henrik Hult, Pontus Braunerhjelm Examiner at KTH: Henrik Hult
TRITA-MAT-K 2017:04 ISRN-KTH/MAT/K--17/04--SE
Royal Institute of Technology School of Engineering Sciences KTH SCI
SE-100 44 Stockholm, Sweden
Abstract
This thesis within Industrial Economics and Applied Mathematics examines the term commodity currency. The thesis delves into analysing the characteristics and consequences of such a currency through a macroeconomic perspective while discussing previous studies within the matter. The applied mathematical statis- tics section audits the correlation between the currency and the commodities of the exporting country through a time series regression. The regression is based on the currency as the dependent variable and the commodities represent the covariates. Furthermore, a trading strategy is developed to see if a profit can be made on the foreign exchange market when looking at the commodity price movements.
Key words: Commodity currencies, regression analysis, time series regression, Dutch disease and trading strategy
Att f¨orst˚a och utnyttja r˚avaruvalutor
En statistisk analys baserat p˚a tidsserieregression
Sammanfattning
Det h¨ar kandidatexamensarbetet ¨ar skrivet inom industriell ekonomi och till¨ampad matematik och granskar termen r˚avaruvaluta (commodity currency). Upp- satsen analyserar, utifr˚an ett makroekonomiskt perspektiv, karakt¨arsdragen och konsekvenserna av en s˚adan valuta, samtidigt som den diskuterar tidigare studier inom ¨amnet. Delen inom till¨ampad matematik unders¨oker korrelationen mellan valutan och r˚avarorna som landet exporterar genom en tidsserieregres- sion. Regressionen ¨ar baserad p˚a valutan som responsvariabel samtidigt som r˚avarorna representerar kovariaterna. Den f¨ardiga modellen anv¨ands sedan i en handelsstrategi som f¨ors¨oker f¨orutsp˚a v¨axelkursens r¨orelser genom att titta p˚a r˚avarornas r¨orelser.
Preface
This Bachelor’s thesis was written in the spring of 2017 by Edward Sikorski and Dylan Dehoky, during their five-year master’s degree program within Industrial Engineering and Management at KTH Royal Institute of Technology. The the- sis combines both aspects from industrial economics and applied mathematical statistics. These aspects were integrated into one report, although the economi- cal and mathematical theories were separated under section 2 and 3 respectively.
We would also like to take the opportunity to thank Joel Berhane, Sara Alexis, Graziella El-Ghorayeb, and Dalill Arafat for their never-withering belief in us.
Lastly, we would like to express our appreciation to our supervisors Henrik Hult and Pontus Braunerhjelm for allowing us to write this thesis together, despite Edward being on the other side of the globe.
Contents
1 Background 1
1.1 Aim . . . . 2
1.2 Research Question and Problem Statement . . . . 2
1.3 Limitations . . . . 2
1.4 Previous Research . . . . 3
2 Theoretical Background 4 2.1 Understanding Exchange Rates . . . . 4
2.1.1 Floating or pegged? . . . . 4
2.1.2 Nominal exchange rate (NER) . . . . 5
2.1.3 Real exchange rate (RER) . . . . 5
2.1.4 Overshooting . . . . 6
2.1.5 Purchasing power parity (PPP) . . . . 6
2.1.6 PPP puzzle . . . . 7
2.1.7 Factors influencing the exchange rate . . . . 7
2.2 Commodity Pricing . . . . 8
2.2.1 Supply and demand . . . . 8
2.3 Commodity Currencies . . . . 9
2.3.1 Commodity currencies through PPP . . . . 9
2.3.2 Consequences of a commodity currency . . . . 10
2.4 Dutch Disease . . . . 10
2.4.1 Historical events . . . . 11
2.4.2 Consequences . . . . 11
2.4.3 Other theories . . . . 12
2.4.4 Mitigation of the phenomenon . . . . 13
3 Mathematical Theory 14 3.1 Multiple Linear Regression . . . . 14
3.2 Ordinary Least Squares . . . . 14
3.2.1 Key assumptions . . . . 15
3.2.2 Lagged variables . . . . 15
3.2.3 Interpretation of the coefficents . . . . 15
3.2.4 Logarithmic transformation of variables . . . . 16
3.3 Time Series Regression . . . . 16
3.3.1 Similarity measure . . . . 17
3.3.2 The Autoregressive model . . . . 18
3.4 Validating the Model . . . . 18
3.4.1 Hypothesis testing . . . . 18
3.4.2 F-test statistics and t-test . . . . 19
3.4.3 p-value . . . . 19
3.4.4 R2and Adjusted R2 . . . . 20
3.4.5 Akaike Information Criterion . . . . 20
3.5 Errors . . . . 20
3.5.1 Heteroscedasticity . . . . 21
3.5.2 Multicollinearity . . . . 22
3.5.3 Endogenity . . . . 23
3.5.4 Normality . . . . 23
3.5.5 Autocorrelation and cross-correlation . . . . 24
3.5.6 Spurious regression . . . . 25
4 Method 27 4.1 Data Collection . . . . 27
4.2 Literature Study . . . . 28
4.3 Choice of Country . . . . 28
4.4 The Regression Model . . . . 29
4.5 Outline . . . . 31
5 Results 33 5.1 Preliminary analysis of the data and unit root analysis . . . . 33
5.2 Cointegration analysis . . . . 35
5.3 Regressions without lag . . . . 36
5.4 Regressions with lag . . . . 38
5.4.1 Smoothed data . . . . 40
5.5 Analysis of models . . . . 42
5.6 Trading results . . . . 46
6 Discussion 49 7 Further Research 53 8 References 54 9 Appendices 58 9.1 Graphs . . . . 58
9.2 Regression outputs . . . . 67
9.3 Nominal Commodity Prices . . . . 68
1 Background
The relationship between macroeconomic fundamentals and the real exchange rate is among the more controversial in the field of international macroeco- nomics. Attempts to model the behaviour of the real exchange rate empirically has repeatedly proven to be unsuccessful. This was most noticeably demon- strated by Meese and Rogoff [1983], where they found a random walk model performing as well as any of their models in predicting the exchange rate. This random walk contradicts the Purchasing Power Theory, which claims that ex- change rates should converge towards an equilibrium level, such that price lev- els are equal once converted to a common currency [Rogoff, 1996]. Voices have been raised that real shocks in macroeconomic fundamentals could prove to be decisive in resolving these empirical puzzles. However, what these price shocks might be, or how to identify and measure them remains to be answered [Chen & Rogoff, 2012].
In contrast, commodity prices have generally been shown to drive real exchange rates in major commodity-exporting countries, giving birth to the term ”com- modity currencies”. One of the first people to discover the correlation between a commodity exporting country and its currency was Paul Krugman [1980], as he observed how oil prices affected different exchange rates. More extensive re- search was made, and economists could confirm the correlation. In 2003, Cashin looked at currencies among developing countries and saw that the correlation was not as robust as with developed countries. The reasons to this was that inflation and capital controls in developing countries in turmoil are constantly fluctuating [Cashin et al. , 2003].
There are several commodity currencies, but studies have shown that the Cana- dian dollars (oil), Australian dollars (gold) and New Zealand dollars (agricul- tural products, e.g. wheat) are the three currencies among developed countries with high correlation to their commodities [Chen & Rogoff, 2002]. Other cur- rencies worth mentioning are the South African Rand (metals, e.g. platinum), Norwegian Krone (oil) and Brazilian Real (oil, soybeans, iron). When the price of a commodity rises, the cost of goods sold increases, thus, resulting in an in- crease of the price. Consequently, this raises inflation. The response to a rise in inflation is a rise in interest rates, in order to strengthen the currency. In essence, appreciation of commodity prices results in a strengthened currency.
However, macroeconomic problems arise along with a commodity currency. The Dutch disease is such an implication, which in simple terms regards how a natu- ral resource boom can cause other sectors, often manufacturing, to experience a decline. The term was coined in the journal The Economist in 1977, describing the decline in The Netherlands’ manufacturing sector following the discovery of oil in the country. This is as the increased commodity export drives up the value of the currency, making the other sectors less competitive on the international market.
Another complication that a commodity currency bears is the sensitivity to fluctuations in the price of the commodity. In the case of developing countries, where a commodity is their main source of income, a fall in the price of their commodity can have dire consequences. For instance, 60% of Mali’s export is gold, leaving them vulnerable to fluctuations in gold prices [OEC, 2015].
However, despite considerable research having been conducted in the field, the majority of the literature concerning the relationship between commodity prices and exchange rates focus on a longer time horizon. This begs the question, from an investors point of view, whether there exists a relationship over a shorter time period.
Hence, this thesis differs from previous studies in the field by seeking to conclude whether there exists a relationship between the nominal exchange rate, instead of the real exchange rate, and commodity prices in selected major commodity currencies on a short term.
1.1 Aim
This thesis aims to assess the short-term relationship between nominal exchange rates and commodities in countries where the majority of the total export con- stitutes of one, or a few, commodities. It further aims to examine, both from a macroeconomic and statistical point of view, the reasons behind the results.
1.2 Research Question and Problem Statement
The aim culminates in the following two problem statements:
• Is there a short-term relationship between commodity prices and nominal exchange rates?
• Is it possible to profit from this relationship?
An Ordinary Least Squares (OLS) estimation will be used for one country, using data from January 2009 until December 2016, to give a robust empirical underpinning to these questions. The OLS method will be defined and discussed in the section Mathematical Theory.
1.3 Limitations
The individual commodity currency selected was the Australian dollar. The currency was selected as Australia is a commodity exporting country, with over 60% of its export consisting of commodities. Furthermore, Australia was specif- ically interesting whilst looking at previous studies within the subject. A more detailed explanation can be found under the section Method. Lastly, data be- tween 2009-01-02 until 2016-12-30 was examined, as data for earlier periods of time were not found for all the commodities.
1.4 Previous Research
In one of the most cited studies in the field, Meese and Rogoff [1983] attempted to compare a variety of structural exchange rate models based on their out- of-sample accuracy. They found that their models failed to forecast country exchange rates more accurately than a random walk model. Even though the structural models based their predictions on actual realized values, they failed to improve on the random walk model.
One of the first to study the correlation in developed countries (Australia, Canada and New Zealand) between prices of their primary commodities and the real exchange rates were Chen and Rogoff [2002]. They found, especially for Australia and New Zeeland, that the price of their commodity exports had a strong influence on their real exchange rates. These results were of a magni- tude in line with predictions of standard theoretical models. Despite this, there was still a purchasing power parity puzzle (PPP puzzle) in the residual when adjusting for commodity price shocks.
Another study conducted in 2003 by Cashin et al. examined the co-movement between real exchange rates in 58 commodity exporting countries and the prices of their commodity exports. They showed a long-run relationship in two-fifths of the countries under study.
Beine et al. [2012], Sachs Warner [2001] and Coudert et al. [2008] all studied the correlation between commodity currencies and their consequences.
Bjørnland and Hungnes [2004] studied the PPP puzzle and showed that once you account for the interest rate differential in the real exchange rate relationship, any deviations from the purchasing power parity are explained for. The study examined Norway, which has oil as its primary commodity, where it constitutes a majority of Norway’s exports. The results are in contrast to previous studies where the PPP puzzle has not been found to hold in the long run. Bjørnland and Hungnes, therefore, claim to have solved the PPP puzzle.
The mentioned reports were studied in order to gain a deeper insight into the dynamics of the currencies. Valuable insight was gained by studying their work, as it helped with the structuring of the problem and mathematical model. The differentiating factor in this thesis compared to previous research will be the mathematical model. This thesis examined the correlation by using daily prices, whilst all prior research used monthly prices.
2 Theoretical Background
This section will discuss the economic theory behind a commodity currency, and what the consequences can be. Different models will be explained, in order to give the reader a deeper insight into commodity pricing and the dynamics of it. A detailed description of the Dutch disease will give a better understanding of the consequences of a commodity currency, and also how to prevent major economical implications for a nation.
2.1 Understanding Exchange Rates
The exchange rate is the rate at which a currency can be exchanged for another [Krugman & Wells, 2013]. It can also be regarded as the price at which curren- cies trade, or the value of one currency in relation to another. These currencies are traded on the foreign exchange (FX) market, where traders can buy and sell currencies. The exchange rate is determined by the supply and demand of a currency and its corresponding equilibrium point. Thus, when the quantity of a currency demanded in the FX market is equal to the supplied quantity, the equilibrium exchange rate has been reached.
2.1.1 Floating or pegged?
A government can choose between different exchange rate regimes in governing toward the exchange rate. It can either implement a fixed or floating exchange rate. [Krugman & Wells, 2013]
A fixed exchange rate means that the rate is pegged to some other cur- rency, usually the US dollar. An early implementation of the fixed exchange rate was the Bretton-Woods system. It was a result of the financial instabil- ity in the world after World War II. The system was a monetary policy that tied countries’ currencies to the US dollar, which was backed by gold. The purpose of this agreement was to end reoccurring and drastic devaluations of currencies in order to gain competitive advantages in the exports market. The system was abruptly discontinued in the so-called ”Nixon shock” in 1971, as the United States could no longer guarantee the value of the dollar to the gold price. [Keylor, 2001]
A modern example of a fixed exchange rate would be the Hong Kong dollar.
Hong Kong has an official policy where the Hong Kong dollar (HKD) has a set exchange rate of 7.80 HKD per USD. However, there might emerge a problem in where the fixed value may not be the natural equilibrium exchange rate between the two currencies on the foreign exchange market. Instead, the HK dollar may either be above or below the target exchange rate. To keep the rate fixed in case of depreciation, the government of Hong Kong has different options. One way is for the government to carry out an exchange market intervention, buying its own currency on the FX market, thus, soaking up the surplus of its own
currency. This requires the government of Hong Kong to have an FX reserve of US dollars to exchange for HK dollars. If the exchange rate is above the target level the government can use the same principle in the reverse direction, selling HK dollars and buying US dollars. [Krugman & Wells, 2013]
In contrast, a floating exchange rate is when the government lets the market forces set the exchange rate based on supply and demand. A majority of the countries in the world employ a floating exchange rate regime.
2.1.2 Nominal exchange rate (NER)
The nominal exchange rate is the price of a currency in terms of another cur- rency, and is the rate that is usually displayed at currency exchanges. They are often quoted in the form of currency pairs. For example, the quotation EUR/USD 1.36 means that 1 euro will buy 1.36 US dollars and 1.36 will thus be the nominal rate from the dollar holder’s perspective, while being 0.735 from the euro holder’s perspective. An exchange rate has a base currency and a counter currency. In our example, the euro is the base currency and the US dollar is the counter currency.
2.1.3 Real exchange rate (RER)
The nominal exchange rate does not necessarily paint the whole picture. It might be of interest to know what can be bought with a certain currency, which is where the real exchange rate comes in. It tries to measure the value of a country’s goods against those of another country, or a set of countries, at the current nominal exchange rate. In general, the RER between two countries is defined as the product of the nominal exchange rate multiplied and the ratio of prices between the countries. The prices are measured by using a broad basket of goods. These baskets take the form of the indices of the aggregate price levels in the countries being compared - such as the consumer price index - making the RER an index number that can be benchmarked through time. The formula for the RER is as follows,
RER = ePY
PX
(1) where e is the exchange rate of currency X in currency Y . PY and PX are the indices of the aggregate price levels in each country. [Krugman & Wells, 2013]
However, researchers, policymakers and economists are normally more inter- ested in the real effective exchange rate (REER). The REER is the average of the bilateral RER:s between the country and the countries it trades with. It is weighted by the respective trade shares of each trading country. The REER of a country can be in equilibrium even though being overvalued compared to some trading partners, as long as it is undervalued relative to others. The REER can be used in assessing whether a currency is misvalued, and if so by how much.
This is done by analysing the REER series over time. If the exchange rates are in equilibrium the REERs should be unchanged over time.
However, fluctuations in the REER does not necessarily imply an underlying misalignment. This is due to consumption patterns, cost for transportation, trade policies and tariffs having the ability to change faster than the market baskets that economists construct. Therefore, not all large REER deviations should be interpreted as misalignments, but at the same time, not all deviations that are not misalignment’s can be attributed to the above-mentioned factors.
Indeed, some REER adjustments are especially smooth, indicating that other factors may be at play. Some of these, especially in higher-productivity coun- tries, can be derived from technological progress which leads to lower production costs on tradables, and thus, lower prices. The international competition leads to lower international prices on said tradables. Yet, theory and data support the notion that the main part of REER variations is due to fluctuations in the prices of non-tradables relative to those of tradables. This is particularly common in developing countries. [Cat˜ao, 2007]
2.1.4 Overshooting
Overshooting is a term used to describe why exchange rates, in most cases, are more volatile than expected. The phenomenon, called the Dornbusch Over- shooting Model, is named after Rudi Dornbusch who introduced the model in his famous paper ”Expectations and Exchange Rate Dynamics”, in 1976.
The model argues that exchange rates will temporarily overreact to alterations in monetary policies, in compensation of rigid prices in the economy. Conse- quently, there will be a higher volatility in the exchange rate as a result of overshooting and the following corrections. [Dornbusch, 1976]
In this thesis, our mathematical model does not account for overshooting. This is as our model looks at how changes in commodity prices affect the exchange rate, excluding changes in monetary policies.
2.1.5 Purchasing power parity (PPP)
First formulated during the sixteenth century in Spain by scholars of the Univer- sity of Salamanca, the Purchasing Power Parity (PPP) is closely related to the theory of the real exchange rate. It states that exchange rates should converge towards an equilibrium level, such that price levels are equal once converted to a common currency [Rogoff, 1996]. It is used to compare different currencies by using a broad market basket of goods and services [Krugman & Wells, 2013].
The currencies are at par when mentioned market basket of goods is priced the same after adjusting for the exchange rate.
For the sake of simplicity, it will be demonstrated in terms of a single prod- uct - the Big Mac sold by McDonald’s Corporation. The Big Mac is a good
example since it is widely available in many countries and almost identical re- gardless of which McDonald’s restaurant in the world you order it from. If the real exchange rate was equal to 1 the price would be the same in the US as in France if sold on the same market. That would be the case if, in using the quotation used before, a Big Mac would cost $1.36 in the US and 1 euro in France. However, if the price of the Big Mac would be higher than 1 euro in France it would suggest that the euro was overvalued, putting pressure on the market and the nominal exchange rate to adjust. This is due to there being an opportunity to exchange euros to dollars in order to buy Big Macs in the US and selling them in France, much according to the law of one price. In practice, it is probably not much to gain in importing or exporting Big Macs, the same can- not be said about tradable commodities, and some of the ingredients in the Big Mac can be regarded as such. Furthermore, although there exist many major obstacles in reality - such as transportation costs, tariffs, trade barriers - curren- cies that diverge in RER face pressure to adapt due to the arbitrage opportunity.
Suppose, for example, that a basket of goods and services that costs $100 in the United States costs 1,000 pesos in Mexico. Then the purchasing power par- ity is 10 pesos per U.S. dollars: at that exchange rate, 1,000 pesos = $100, so the market basket costs the same amount in both countries. Calculations of purchasing power parities are usually made by estimating the cost of buying broad market baskets containing many goods and services — everything from automobiles and groceries to housing and telephone calls.
2.1.6 PPP puzzle
The concept of PPP was revived in the during the 1970s. Since then, the theory’s validity has been highly debated among economists and scholars, making it the PPP puzzle. Even though the theory claims that any deviations should only be minimal or momentary, empirical work supporting the PPP was weak [Taylor & Taylor, 2004]. Indeed, while few economists view the PPP seriously in the short-term, most regard the PPP, or a variant of it, as an anchor for long-term real exchange rates. This is as real exchange rates go extremely slowly towards PPP, as deviations from the equilibrium decrease by 15% per year. The long-term believers argue that there are frictions in the international trade goods market, which as previously mentioned are transportation costs, tariffs, etc. [Rogoff, 1996].
2.1.7 Factors influencing the exchange rate
Inflation and interest rates are two important factors that can both appre- ciate and depreciate the exchange rate. The two factors work hand in hand, as central banks use the interest rate to steer inflation. High interest rates usually attract foreign investment, which leads to an increased demand for a country’s currency (and an increased exchange rate). Nonetheless, central banks are care- ful as high interest rates raises inflation, which appreciates the currency. On the
other hand, low interest rates boost economic growth and consumer spending, although it does not attract foreign investments. Hence, inflation and interest rates are difficult to manage, while having a great influence on a country’s cur- rency. [Krugman & Wells, 2013]
In order to afford financing of public sector projects and governmental fund- ing, countries usually take on debt. Public debt may stimulate the domestic economy, however, large public deficits make countries less attractive to foreign investments. This is due to the fact that debt stimulates inflation, thus de- preciating the real exchange rate. Consequently, a high inflation will make it difficult for the country to pay off their debt with their cheaper real currency.
[Beningo & L´opez-Salido, 2004]
Terms of trade is another explanation for a rise in the exchange rate. It is the ratio of a country’s import and its export. Essentially, it measures how much an economy can import per unit of exported goods. A banal exemplification would be if a country were to only export oil, while also only importing wheat. The terms of trade would simply be the price of oil divided by the price of wheat [Reinsdorf, 2009]. An appreciation in the prices of exported goods would in- crease the country’s terms of trade, while a rise in the prices of imported goods would lower it. Research conducted by Coudert et al [2008] confirmed the link between the REER and the commodity terms of trade. In the long run, the price elasticity between the two terms was found to be 0.5. In simpler terms, a 10% appreciation in terms of trade implies a 5% rise of the REER.
Political stability is an important factor that investors seek in a currency.
A country with such stability will draw investments away from countries that are in a less optimal situation. Political turmoil, elections and other political situations can cause a movement of capital to more stable currencies.
2.2 Commodity Pricing
Whether if it is the manufacturing industry or the service industries, commodi- ties are omnipresent. Commodities are essential for the entire economy as a whole. Therefore, it is important to understand the characteristics of a com- modity and its pricing.
2.2.1 Supply and demand
According to basic microeconomic theory, supply and demand are the two fac- tors that determine the price. A decrease in demand or increase in supply lowers the price of the commodity. Vice versa, an increase in demand or decrease in supply raises the price [Krugman & Wells, 2013]. The supply and demand of a product can be changed by various different factors. The finding of a new source of the resource would alter the supply, while the demand would be affected if a substitute product emerges.
Economists attempt to predict commodity price movements by looking at lead- ing indicators. Interest rates and inflation are leading economic indicators, and are commonly used to predict movements. Within commodity pricing, potential leading indicators would be investments, government spending, con- sumption and net exports [Krugman & Wells, 2013]. However, what differs a commodity currency from the rest is the impact that the commodities have on the currency, which lessens the impact of the other economic factors.
2.3 Commodity Currencies
Firstly, it is worth mentioning that there is no precise definition of a commodity currency. Currently, the definition of a commodity currency is when a country’s export is heavily dependent on one or more commodities. In other words, there is no set percentage of the country’s export that has to consist of commodities for it to be defined as a commodity currency. The currencies are most common in developing countries, although they do also exist in developed nations. Chen and Rogoff [2002] studied the commodity currencies of three developed countries:
Canada, Australia and New Zealand. The results showed that commodity prices had a strong influence on the REER. However, the impact of the commodity was less for the Canadian dollar, as Canada’s export was more diversified than the other two countries.
2.3.1 Commodity currencies through PPP
As mentioned in the section PPP Puzzle, there has been an ambiguity regarding the PPP. In 1976, Professor Dornbusch’s overshooting model showed clearly that inflation and monetary instability could not explain the entire truth of the per- sistent exchange rate volatility. The standard monetary models failed to grasp the whole situation, as they were unable to explain the slow rate at which devia- tions from the PPP seemed to die out, even though the real exchange rates were volatile. In essence, shocks in taste, technology or other similar factors could not account for the short-term fluctuations in exchange rates. Thereupon, Rogoff found a potential solution to the PPP puzzle by examining commodity curren- cies. Commodities could provide a shock that is both volatile, persistent and reoccurring. [Chen & Rogoff, 2002]
In 2002, Chen and Rogoff claimed that their univariate regressions suggested that the missing shock was the volatile commodity prices. By examining three commodity-exporting developed countries, they could identify that commodities explained a significant contribution to the PPP puzzle. However, the introduc- tion of commodities did not resuscitate the monetary approach to the exchange rate, despite being a dependable explanatory factor. Consequently, a year later, Cashin et al proved the same result in a third of the 58 countries they examined.
[Cashin et al. , 2003]
Bjørnland and Hungnes examined the PPP puzzle and introduced an interest rate differential in their calculations. They noticed that the differential caused the correlation between commodities and currencies to decrease, which was to be expected. However, they detected that adjustments to shocks from the equi- librium took maximum a year on average, which argues for the validity of PPP [Bjørnland & Hungnes, 2005]. Consequently, they argue that the puzzle has been solved for the commodity currency, if taking the interest rate into account.
2.3.2 Consequences of a commodity currency
The consequences of a commodity currency are that if the commodity experi- ences a decline in price, the income from exporting that commodity decreases along with the price. Hence, the dependence of a single commodity bears heavy risk. Canada and its reliance on oil is a great example. During 2015, oil prices fell 38%, resulting in the Canadian oil industry to post losses of 11 billion Canadian dollars. In 2016, the same trend continued [Murillo, 2016]. As the oil prices dipped below 30 USD per barrel in 2016, Bank of Canada governor Stephen Poloz stated that the drop in oil prices have caused a 50 billion Canadian dollar cut to Canada’s national income. This equates to $1500 a year per capita for the nation [Kirby et al. , 2016]. Another consequence of having a commodity currency could be the Dutch disease.
2.4 Dutch Disease
The Dutch disease is an economic phenomenon first described by economists W.
Max Corden and J. Peter Neary in 1982, published in the Economic Journal.
The phenomenon describes the negative effects that follow a large increase in the value of the country’s natural resources, which causes a decline in other parts of the economy. It affects three sectors: the non-tradable sector, the boom- ing (tradable) sector, and the lagging sector. The non-tradable sector includes services (i.e. labour), while the booming sector represents the newly-found ex- traction of natural resources (oil, gold, diamonds, etc). The lagging sector is usually a reference to manufacturing or agriculture, in other words, industries with heavy use of labour. [Corden & Neary, 1982]
Initially, the Dutch disease begins with a new found source of natural resources or increases in commodity prices, which causes the revenues of the booming sector to increase rapidly. Consequently, the real exchange rate of the country appreciates. This appreciation of the exchange rate impedes other sectors, as their exports become more expensive for other countries to buy. Also, imports for these sectors become cheaper, resulting in those sectors being less competi- tive. This is in line with what we described for a commodity currency.
What the Dutch disease specifically addresses is that a resource boom has two main consequences for the non-tradable sector. Firstly, the resource boom in- creases demand for labour, causing production to shift from the lagging to the
booming sector. This alteration is called direct-deindustrialization.
The second development is called the indirect-deindustrialization, or the ”spend- ing effect”. It is a result of the extra revenue gained by the resource sector, which raises demand for labour in the non-tradable sector at the expense of the lag- ging sector. The increased demand within the non-tradable sector raises the prices within non-tradables. However, the prices in the tradable sector are un- changed, as they are set on the international market. This causes the REER to appreciate. The indirect-deindustrialization occurs if there is no labour mobility between sectors, as it obstructs the alteration in the supply of services to shift in demand. Hence, if such a mobility exists it allows the supply of services to adjust. Consequently, workers can move between sectors, which forces all sec- tors to increase wages. As previously mentioned, the result is that the tradable sector can not raise their prices to mitigate the pay rise, resulting in a decline in manufacturing output and employment. [Corden & Neary, 1982]
2.4.1 Historical events
In 1959, large gas reserves were discovered in the Netherlands, causing Dutch exports to soar. As per the definition of the disease, the booming sector thrived while another sector lagged. Moreover, between 1970 to 1977, there was a rise in unemployment from 1.1% to 5.1% and corporate investment was crashing.
The sudden boom of gas exports raised the value of the Dutch currency, making other sectors less attractive on international markets. Moreover, the gas extrac- tion industry generated few jobs, while also being a capital-intensive sector. To hinder the Dutch currency from appreciating rapidly, the Dutch central bank implemented low interest rates. In turn, this removed future economic potential in the country as investments vanished. [Kiev, 2014]
In modern time, there have been several cases of potential Dutch diseases. Most of the cases involve developing countries, such as Burundi, Tanzania and Papua New Guinea. More renown cases of the Dutch disease in developed countries would be the rise of oil prices in 2014 and the impact on Canada. The rise in the price of the commodity, as Canada exploited their oil sands, led to an overvalued Canadian dollar. Consequently, this lowered competitiveness in the manufacturing sector. [Tencer, 2014]
2.4.2 Consequences
The consequences of the Dutch diseases are similarly considered to have a great impact on a country’s economy. To continue on the case of the appreciation of oil prices and Canada, the consequences were a profitable oil extraction method and a contracted manufacturing sector [Beine et al. , 2012]. However, it is no- table that the oil price fall in 2015-2016 eased the concerns of Dutch disease in Canada. This ease was at the expense of the Canadian economy, as the Canadian export income lost $50 billion dollars. Hence, it is not entirely clear
whether which consequence has the greatest impact.
Overborrowing is a potential effect of the Dutch disease. A prosperity of resources along with high commodity prices can allow countries to use their resources to borrow capital to finance large investments. However, when prices plunge, countries are left with huge unsustainable debts while their resource has lost in value.
Volatility is usually high for commodities, as the supply elasticity for these resources usually are low. In turn, if the commodities’ volatility is low and a great portion of the export income derives from commodity exports, it will drive the volatility of the real exchange rate. Empirical work has shown that there is a detrimental impact on economic performance. [Loayza et al. , 2007]
Lastly, declined GDP growth is caused by the abundance of resources. Stud- ies by Sachs and Warner [2001] show that a finding of natural resources has a negative impact on GDP growth. They state that a 10% increase in the ratio of national resources to GDP can lower the GDP growth by 0.4-0.7%. Addi- tionally, they found that it reduced manufacturing export growth. However, Lederman and Xu [2015] argue that these findings are not entirely conclusive as they do not take all factors into consideration. They claim that the the findings do not have grounded economic theory to back their measure of natural resource abundance. Instead, Lederman and Xu used another approach by examining the net exports of natural resources per worker, and could thus find a positive effect on growth.
2.4.3 Other theories
There are theories that conflict with the Dutch disease. The main contradic- tory theory would be the Balassa-Samuelson (B-S) hypothesis which is an- other explanation for the appreciation of the REER. The effect tends to occur in developing economies, as they begin using their land, labour and capital in a more efficient manner. A rise in productivity gives way to wage growth in both the tradable goods and the non-tradable goods sectors. This wage rise al- lows citizens to consume more goods and services, which in turn push up prices and consequently inflation. According to the B-S hypothesis, high productiv- ity growth in the tradable sector relative to the non-tradable sector causes an appreciation of the REER, due to increased inflation. The larger the differ- ence in productivity growth between the sectors, the faster the REER rises.
[Druˇzi´c & Tica, 2006]
These theories are viable, as it can be difficult to identify a lagging sector with the Dutch disease, and as there could be various other factors causing the lagging sector to decline.
2.4.4 Mitigation of the phenomenon
Fiscal policy, i.e. how a government can adjust its tax rates and spending lev- els to influence its nation’s economy, is a way to reduce the impact of the Dutch disease. Researchers analysed the natural resource boom during the 1970s and 1980s, and concluded that spending levels should have been adjusted more cau- tiously to the sharp rises in income [Gelb & Associates, 1988]. The reason why fiscal policy is an important instrument way to deal with the Dutch disease is mainly because it can constrain the spending effect while smoothing expen- ditures to reduce the volatility. Governments can save the revenue abroad in sovereign wealth funds and thus reduce aggregate spending. A lot of commodity dependent countries have adopted this fiscal policy, for instance the following sovereign wealth funds have the purpose of mitigating the Dutch disease: State Oil Fund of Azerbaijan, Stabilization Fund of the Russian Federation, Govern- ment Pension Fund in Norway and the Australian Government Future Fund.
However, all countries cannot adopt this policy. Developing countries can not af- ford to keep revenues abroad during a longer time, as factors such as health care and education require funds. The need to allay poverty stands as more impor- tant than any macroeconomic implication. Lastly, within the government’s fiscal policy, a strategy to avoid appreciation of the REER is to increase saving in the economy. This would decrease large capital inflows which increases the REER.
This would be achieved by running a budget surplus. [van Wijnbergen, 2008]
The ”permanent income approach” is an important benchmark for fiscal policy.
It can only be applied to expendable resources, and proposes to first calculate the net present value of the net future revenues from these resources. Then, it proposes to calculate the constant real amount or annuity that received in perpetuity, would yield the same net present value. The method recommends to restrict government spending using the expendable natural resource revenues to this annuity, and saving the rest of the revenues overseas. Further down the road, when the natural resources have run out or depreciated in value, the government is able to withdraw the financial assets and continue spending on the same annuity level. [van Wijnbergen, 2008]
Another way to curb the Dutch disease is to revise the country’s spending poli- cies. As mentioned, the non-tradable sector declines during the phenomenon.
However, by investing funds in the sector, ensures that productivity in the sec- tor improves which is important. Alleviating the pressure from the non-tradable sector could be a structural way to respond to the Dutch disease. Moreover, a policy that would stimulate demand for imports, which would increase the terms of trade, would diminish demand pressure and also any future implication. In- vestments in transport, logistics, infrastructure and education could mitigate the adverse effects of a natural resource boom. It could benefit the productivity while also help fight poverty. However, as mentioned earlier, it is important to ensure that there are enough funds for public projects with the sole purpose of assuaging poverty in low income countries.
3 Mathematical Theory
Regression analysis is used as a statistical tool. The main purpose is to estimate the relationship between a section of covariates and a dependent variable. This will be explained further in the section.
3.1 Multiple Linear Regression
The definition of a multiple linear regression model is given by:
yi=
k
X
j=0
xijβj+ ei, i = 1, ..., n, (2)
where yi are observations of the dependent random variable. The value of yi
depends on the covariates, xij and the residual or error term ei. The beta’s, βj, also called the coefficients, are the terms to be determined from running the regression. Lastly, there are k explanatory variables and n observations. The model can also be written with matrix notation as follows
Y = X ~~ β + ~e (3)
with the following vectors
Y =~
y1
... yn
, β =~
β0
... βk
~e =
e1
... en
and the matrix
X =
1 x1,1 ... x1,k
1 x2,1 ... x2,k
... ... . .. ... 1 xn,1 · · · xn,k
[Lang, 2016]
3.2 Ordinary Least Squares
The Ordinary Least Squares (OLS) method is commonly used to conduct a multiple linear regression on a set of a data. The method calculates the value of α and β from equation 2, by minimizing the sum of the squared residuals.
The residuals are squared in order to remove the possibility that positive and negative residuals cancel each other out. There are some requirements for the method to be successful, which will be explained further in the subsection below.
3.2.1 Key assumptions
In order for the Ordinary Least Squares (OLS) estimator to show relevant re- sults; the following assumptions are made:
1. The dependent variable is a linear function of the covariates and the resid- ual.
2. The expected value of the residual is equal to zero E[ei] = 0.
3. Perfect multicollinearity is nonexistent, as the covariates are linearly in- dependent.
4. The residuals have variance V [ei|X] 6= Iσ2, and are uncorrelated, Cov(ei, ej) = 0, for i 6= j.
Under violation of these assumptions, the model would need altering. The method of modification will be described in a different subsection in the chapter named Errors. [Kennedy, 2008]
3.2.2 Lagged variables
In general, regression analysis is considered timeless, as it does not take time into account. Further, in regression the dependent y-variable is influenced by prior y-values. This can be overcome by using lagged dependent variables. The aim of lagged variables is to provide more accurate coefficient estimates. These models, so-called partial adjustment models, are formulated as following:
Yt= β0+ β1Yt−1+ β2X1t+ . . . + βnXnt+ et. (4) Moreover, independent variables, xi, are possible to lag. However, this often increase the level of difficulty noticeably. Also, the contribution to the model is only a fraction of the level of difficulty. Another effect that previous studies have shown is that estimated lagged effects can irritate the bias and lead to further collinearity between covariates [McKinnish, 2002].
3.2.3 Interpretation of the coefficents
Ceteris paribus means ”other factors being equal”, and is a key notion in causal analysis. It is used in order to screen out factors that may influence the relation of interest, by holding all other factors that may influence this relationship fixed. For example, lets assume one would like to investigate the change of demand of a certain good after a price change, while holding all other factors that may influence the change of demand fixed. These factors could be income, individual tastes, price of substitute goods, etc. If these factors are not held fixed, the causal effect of a price change of the goods will be impossible to measure. [Kennedy, 2008]
3.2.4 Logarithmic transformation of variables
Not all models follow a linear model, thus, requiring a transformation of vari- ables to be implemented. There are various different transformations, such as the power transformation or the logarithmic transformations. Choosing the correct transformation is often difficult since it is hard to know the true model of the observed values on beforehand. However, in this thesis, the logarithmic transformation was used.
Regarding the logarithmic transformation, there are three different ways in- volving logarithms: the log-linear, linear-log and log-log model. This thesis uses the log-linear transformation, i.e.
log(yi) = xiβi+ ei (5)
The logarithmic transformation is used when there exists a non-linear relation- ship between the dependent and independent variables. Also, the transforma- tion can be used when dealing with a highly skewed variable that has to be transformed into a more appropriate one. Also, logarithmic transformations have a variance reducing effect. [Aneuryn-Evans & Deaton, 1980]
3.3 Time Series Regression
The cross-sectional data described above differs from time series data. The most obvious difference is temporal ordering, which means that one must recognize that the past can affect the future, but the future cannot affect the past. Thus, time series data can be of great use, as this is how the stochastic process of a commodity’s price fluctuates. However, one has to be cautious when conducting the time series regression. The correlation between the independent and depen- dent variable can distort the OLS large sample properties. [Woolridge, 2009]
There are six assumptions for time series regression, namely:
1 Linear in parameters
This implies that the stochastic process (xt1, ..., xtk, yt): t = 1, 2, ... , n follows the linear model:
yt= β0+ β1xt1+ ...βkxtk+ ut (6) where utis the term of error. n represents the number of observations.
2 No perfect collinearity
No covariate is constant, or a perfect linear combination of the other covariates.
3 Zero conditional mean
At each t, the expected value of ut, given that all the explanatory variables for all time periods are available, is equal to zero.
E[ut|X] = 0, t = 0, 1, 2, ..., n (7)
4 No serial correlation
The errors at two different times are uncorrelated, conditioned on X.
Corr[ut, us|X] = 0 (8)
5 Homoscedacity
Conditional on X, the variance utis the same for all times t.
V ar[ut|X] = σ2, t = 1, 2, ..., n (9) 6 Normality
The errors ut are independent of X and identical and independently dis- tributed random variables with a normal distribution with mean 0 and variance σ2.
3.3.1 Similarity measure
To study the linear relationship between two time series and the sample cor- relation, equation (31), can be used. An alternative measure of the similarity between two time series is based on the Euclidean metric, defined as follows,
DX Y = 1 T
T
X
t=1
(xt− yt)2 (10)
By expanding the square on the right hand side, familiar quantities can be extracted from the compact form in equation (10)
DX Y = 1 T
T
X
t=1
(xt− yt)2
= 1 T
T
X
t=1
[(xt− ¯x) − (yt− ¯y) + (¯x − ¯y)]2
= 1 T
T
X
t=1
(xt− ¯x)2+ 1 T
T
X
t=1
(yt− ¯y)2
+ (¯x − ¯y)2− 2 T
T
X
t=1
(xt− ¯x)(yt− ¯y)
(11)
where ¯x and ¯y are the sample means of the respective series. The two first terms are the sample variance of each series, while the last is sample covariance (compare to equation (31)). Dividing both sides of the equation with the square root of the sample variance turns the third term into equation (32). Compared to the simple cross-correlation, this measure also takes the variance of each series into account, as well as the difference in their means. Note that the measure in equation (10) is sensitive to the scaling of the variables but can be made invariant by using a modified measure, calculated using the terms on the right hand side equation (11), divided by the appropriate terms.
3.3.2 The Autoregressive model The AR(p) model is defined as
Xt= c +
p
X
i=1
φiXt−i+ t (12)
where c is a constant, φ1, . . . , φp are the parameters of the model and t is a zero-mean white noise process. The simplest instance of this process is the AR(1) process, given by
Xt= c + φXt−1+ t (13)
For this process, the mean and variance are given by E(Xt) = c
1 − φ, V ar(Xt) = σ2
1 − φ2 (14)
In particular, if c = 0 then the mean of the process is zero. The autocovariance of the AR(1) process is given by
Cov(Xt+h, Xt) = σ2
1 − φ2φ|h| (15)
From the expression for the variance in equation (14), the autocorrelation is easily obtained as
Corr(Xt+h, Xt) = Cov(Xt+h, Xt)
V ar(Xt) = φ|h| (16)
The parameters of the model can be estimated using OLS.
3.4 Validating the Model
The validation of a model is necessary before it can be used. The method of validating a model is by using statistical tests and theories, which will be described in the subsections below.
3.4.1 Hypothesis testing
Hypothesis testing is used to study a set of parameters, allowing conclusions to be made. There are three steps in testing a hypothesis. [Uriel, 2013].
1. Formulate a null hypothesis H0specifying a value to βj, and an alternative hypothesis H1.
2. Compose a test statistic with a known distribution under the assumption that H0is valid.
3. From this test statistic, rule whether to reject H0 or not.
