Understanding and Exploiting Commodity Currencies a Study Using Time Series Regression

DEGREE PROJECT IN TECHNOLOGY, FIRST CYCLE, 15 CREDITS STOCKHOLM, SWEDEN 2017

Understanding and Exploiting commodity currencies A Study using time series Regression

DYLAN DEHOKY

EDWARD SIKORSKI

KTH ROYAL INSTITUTE OF TECHNOLOGY SCHOOL OF ENGINEERING SCIENCES

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 URL: www.kth.se/sci

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 statistics 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˚aoch utnyttja r˚avaruvalutor En statistisk analys baserat p˚atidsserieregression

Sammanfattning

Det härkandidatexamensarbetet ärskrivet inom industriell ekonomi och tillämpad matematik och granskar termen r˚avaruvaluta (commodity currency). Upp- satsen analyserar, utifr˚anett makroekonomiskt perspektiv, karaktärsdragen och konsekvenserna av en s˚adanvaluta, samtidigt som den diskuterar tidigare studier inom ämnet.Delen inom tillämpadmatematik undersöker korrelationen mellan valutan och r˚avarorna som landet exporterar genom en tidsserieregres- sion. Regressionen ärbaserad p˚avalutan som responsvariabel samtidigt som r˚avarorna representerar kovariaterna. Den färdigamodellen användssedan i en handelsstrategi som försöker förutsp˚aväxelkursensrörelsergenom att titta p˚a r˚avarornas rörelser.

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 thesis combines both aspects from industrial economics and applied mathematical statistics. These aspects were integrated into one report, although the economical 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 R2 and 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 demonstrated 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 exchange rates should converge towards an equilibrium level, such that price levels 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 ”commodity 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 research 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 currencies 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 increase 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 natural 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.

1 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 constitutes 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 specifically interesting whilst looking at previous studies within the subject. A more detailed explanation can be found under the section Method. Lastly, data between 2009-01-02 until 2016-12-30 was examined, as data for earlier periods of time were not found for all the commodities.

2 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 magnitude 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.

3 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 currencies 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 currency, usually the US dollar. An early implementation of the fixed exchange rate was the Bretton-Woods system. It was a result of the financial instability 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

4 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 currency, 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, P RER = e Y (1) PX 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.

5 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 countries, 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. [Catão,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 product - the Big Mac sold by McDonald’s Corporation. The Big Mac is a good

6 example since it is widely available in many countries and almost identical regardless 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 cannot 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 - currencies 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 parity 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 appreciate 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

7 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 currency. [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 & López-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 increase 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, commodities are omnipresent. Commodities are essential for the entire economy as a whole. Therefore, it is important to understand the characteristics of a commodity and its pricing.

2.2.1 Supply and demand According to basic microeconomic theory, supply and demand are the two factors 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.

8 Economists attempt to predict commodity price movements by looking at leading 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, consumption 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 persistent exchange rate volatility. The standard monetary models failed to grasp the whole situation, as they were unable to explain the slow rate at which deviations 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 currencies. 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 introduction 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]

9 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 equilibrium 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 booming (tradable) sector, and the lagging sector. The non-tradable sector includes services (i.e. labour), while the booming sector represents the newly-found extraction 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 competitive. 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 increases demand for labour, causing production to shift from the lagging to the

10 booming sector. This alteration is called direct-deindustrialization.

The second development is called the indirect-deindustrialization, or the ”spending 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 lagging sector. The increased demand within the non-tradable sector raises the prices within non-tradables. However, the prices in the tradable sector are unchanged, 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 sectors 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 extraction 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

11 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 another 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 allows citizens to consume more goods and services, which in turn push up prices and consequently inflation. According to the B-S hypothesis, high productivity growth in the tradable sector relative to the non-tradable sector causes an appreciation of the REER, due to increased inflation. The larger the difference in productivity growth between the sectors, the faster the REER rises. [Druˇzić& 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.

12 2.4.4 Mitigation of the phenomenon Fiscal policy, i.e. how a government can adjust its tax rates and spending levels 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 afford 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 important 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 policies. As mentioned, the non-tradable sector declines during the phenomenon. However, by investing funds in the sector, ensures that productivity in the sector 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.

13 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:

k X yi = xijβj + ei, i = 1, ..., n, (2) j=0 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~ = Xβ~ + ~e (3) with the following vectors       y1 β0 e1 ~  .  ~  .   .  Y =  .  , β =  . ~e =  .  yn βk en and the matrix   1 x1,1 ... x1,k 1 x2,1 ... x2,k  X =   . . .. .  . . . .  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.

14 3.2.1 Key assumptions In order for the Ordinary Least Squares (OLS) estimator to show relevant results; the following assumptions are made:

1. The dependent variable is a linear function of the covariates and the residual.

2. The expected value of the residual is equal to zero E[ei] = 0. 3. Perfect multicollinearity is nonexistent, as the covariates are linearly independent.

2 4. The residuals have variance V [ei|X] 6= Iσ , 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]

15 3.2.4 Logarithmic transformation of variables Not all models follow a linear model, thus, requiring a transformation of variables 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 involving 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 relationship between the dependent and independent variables. Also, the transformation 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 dependent 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 ut is 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)

16 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 ut is the same for all times t. 2 V ar[ut|X] = σ , t = 1, 2, ..., n (9)

6 Normality The errors ut are independent of X and identical and independently distributed 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 correlation, equation (31), can be used. An alternative measure of the similarity between two time series is based on the Euclidean metric, deﬁned as follows,

T 1 X D = (x − y )2 (10) XY T t t t=1 By expanding the square on the right hand side, familiar quantities can be extracted from the compact form in equation (10)

T 1 X D = (x − y )2 XY T t t t=1 T 1 X = [(x − x¯) − (y − y¯) + (¯x − y¯)]2 T t t t=1 (11) T T 1 X 1 X = (x − x¯)2 + (y − y¯)2 T t T t t=1 t=1 T 2 X + (¯x − y¯)2 − (x − x¯)(y − y¯) T t t t=1 wherex ¯ andy ¯ 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.

17 3.3.2 The Autoregressive model The AR(p) model is deﬁned as

p X Xt = c + φiXt−i + t (12) i=1 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

c σ2 E(X ) = , V ar(X ) = (14) t 1 − φ t 1 − φ2 In particular, if c = 0 then the mean of the process is zero. The autocovariance of the AR(1) process is given by

σ2 Cov(X ,X ) = φ|h| (15) t+h t 1 − φ2

From the expression for the variance in equation (14), the autocorrelation is easily obtained as

Cov(Xt+h,Xt) |h| Corr(Xt+h,Xt) = = φ (16) V ar(Xt) 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 H0 specifying a value to βj, and an alternative hypothesis H1. 2. Compose a test statistic with a known distribution under the assumption that H0 is valid.

3. From this test statistic, rule whether to reject H0 or not.

18 3.4.2 F-test statistics and t-test The F-test is suited for more rigid models. It tests model relevance of several coeﬃcients at once, in other words the hypotheses: ˆ H0: βi = 0 for i > 1 ˆ H1: βi 6= 0 for i > 1 The following expression is the F-variable and its distribution.

n − k − 1|eˆ |2 F = ∗ − 1 ∈ F(r, n − k − 1). (17) r |eˆ|2

The null hypothesis, H0 is rejected if F is larger than the distribution on the right hand side of equation 17, proving that the model is signiﬁcant. Further,e ˆ represents the residual from the unrestricted model.e ˆ∗ symbolizes the residual from the restricted model, where r is the amount of β:s that are set to be equal to zero. n is the amount of observations while k represents the amount of parameters in the model. [Lang, 2016, p.10]

An alternative method to the F-test, is the t-test that is relevant when there is only a single restriction to the model. Also, it tests whether the β-value is signiﬁcant. In the same null hypothesis as mentioned above, the test statistic should follow a t-distribution. The t-distribution can be seen as the following:

βˆ − β t = i i ∼ t , (18) ˆ n−k SE(βi) ˆ βi represents the estimation of one of the covariates. βi is a constant, while ˆ ˆ SE(βi) is the sampled standard error of βi. The t is t-distributed with n−k −1 degrees of freedom.

3.4.3 p-value The before-mentioned F-test is essential in generating the p-value, that is given by: p = P r(F > X), (19) X is a F (r, n − k − 1) distributed random variable, while F is the test statistic. The null hypothesis is accepted if the p-value is greater than the predetermined signiﬁcance level α. [Lang, 2016, p.10] In this thesis, α = 5% will be used as the signiﬁcance level.

19 3.4.4 R2 and Adjusted R2 The coefficient of determination, i.e. R2, measures the ”goodness of fit” meaning how well the model fits the data points. R2 has a range between [0, 1], where value 1 implies that the model can to 100 per cent explain the variability of the observations around the mean. The formula for R2 is the following:

P 2 2 i(yi − yˆi) R = 1 − P 2 . (20) i(yi − y¯) The adjusted R2 takes into account the downside of the regular R2. This downside is that R2 increases when adding more dependent variables, regardless if they have any explanatory power [Lang, 2016, p.8-9]. In the equation below, it is visible that the adjusted R2 is altered by the degree of freedoms, resulting in a lower value than the ordinary R2.

P 2 (yi − yˆi) ¯2 n − 1 i R = 1 − · P 2 (21) n − k − 1 (yi − y¯i) i

3.4.5 Akaike Information Criterion An information criterion can be used when choosing between similar models. The Akaike Information Criterion test (AIC) is a widely adopted tool, which uses the equation below. [Lang, 2016, p.22]

− 2 ∗ ln(Lˆ) + 2k (22)

In the equation above, k represents the amount of covariates, the residuals and n the sample size. Lˆ is the maximized value of the likelihood function. [Lang, 2016]. The AIC allows us to perform model selection, by comparing the calculated AIC value for the proposed model. The best model, in the sense that it minimises the information loss relative to the true data-generating model, is the one with the smallest value for the AIC. As the true model is not known, the AIC is an estimate of the information loss.

3.5 Errors The estimator will give inconsistent results if the key assumptions of the Ordi- nary Least Squares (OLS) model are breached. Consequently, the model would need altering. This section will present the different kinds of violation, along with different methods of reducing their effect.

20 3.5.1 Heteroscedasticity Homoscedaticity is one of the key assumptions of the OLS, and heteroscedaticity violates it. It occurs when the residuals do not have constant variance, i.e.

2 V ar(ei) = σi , (23)

Under this violation, the error term is heteroscedastic and requires modification in order to fulfill the assumption of homoscedaticity. Otherwise the standard deviations of the coefficient estimates will be incompatible, rendering the F-test invalid. This would result in inconsistent estimates. [Lang, 2016, p.16]

Diﬀerent techniques to mitigate heteroscedaticity will be presented below.

Reformulate the Model The best way to remove heteroscedacity is by reformulating the model. This can either by done by adding covariates or transforming the variables in the model. This thesis looks at speciﬁc covariates’ correlation with the dependent variable, and utilizes transformation of variables.

Breusch-Pagan test The Breusch-Pagan test is used to test for conditional heteroscedaticity. The method involves testing if the estimated variance V ar(ˆe) is dependent of the covariates in the model. If the estimated variance is dependent on the covariates, the model is heteroscedastic.

2 As previously mentioned, an assumption for homoscedaticity is that E[ei ] = 2 σi , which implies that the variance is not dependent on the covariates. In order to conduct the Breusch-Pagan test, the variance of the model is needed, which can be obtained by taking the average of all squared terms of error eˆ2. Further, a regression is conducted on eˆ2 as a dependent variable with the covariate X.

ˆe2 = βX + u (24) where u is the model’s term of error. Moving on, one can test H0 (homoscedastic model) against H1 (heteroscedastic model) with use of a F-test. If the F-test can prove that the variables are jointly signiﬁcant, then one can reject H0, proving that the model is homoscedastic. [Woolridge, 2009]

Residual vs Fitted A useful method to identify heteroscedaticity is by using plots. The plot is composed by seeing how residuals on the y-axis ﬁt along with the estimated responses on the opposite axis. If the points are in the vicinity of the zero line, it proves homoscedastic data.

21 White’s consistent variance estimator

ˆ t −1 t 2 t −1 Cov[β] = (X X) X D(e ˆi )X(X X) (25)

2 where D(e ˆi ) is a diagonal nxn-matrix with the diagonal elementse ˆi, i = 1, 2, . . . , n. When employing White’s method, the standard errors are estimated from the equation above, and the regression is still implemented using the OLS method. The standard error of the i:th diagonal element can be written as: q Cov[βˆ] = p(XtX)−1s2 (26)

2 2 |eˆ | where s = n−k−1 [White, 1980]

3.5.2 Multicollinearity Multicollinearity results in difficulties in identifying the effects of the explanatory variables on the dependent variable. This issue emerges when two or more covariates are approximately linearly dependent. Furthermore, the variances of the regression coefficients are contrasting large under multicollinearity, which results in incorrect estimate points.

To avoid this error, the covariates have to be selected carefully. For example, including dummy variables for all conceivable cases can naturally lead to linear dependence causing multicollinearity. As multicollinearity causes high variances of regression coefficients, a method to identify this error is by inves- tigating covariates variances. A commonly used method is by examining the Variance Inflation Factor (VIF). It is defined as: 1 VIF = 2 (27) 1 − Ri This factor displays how much the variance of the i:th covariate has increased as a result of multicollinearity. A VIF > 10 indicates that multicollinearity is evident. [Lang, 2016, p.55]

However, there are ways to compensate for large VIF values. One way to reduce this variance is by gathering additional data for the regression, as this results in a decreased variance. This is as the standard error of the coeﬃcients depends on the amount of observations, seen in the following formula. s σˆ2 1 SE(βˆ ) = · , (28) i ˆ p 2 (n − 1)V (xi) 1 − Ri

22 3.5.3 Endogenity Endogeneity emerges if the residual is correlated with one or more of the covariates. The key assumption that the expected value of the error term is equal to zero is thus breached, causing the OLS estimator to emit inconsistent values. This subsection will go through common causes of this error.

Simultaneity The emergence of simultaneity is caused when a covariate is aﬀected by the dependent variable, while also inﬂuencing the dependent variable. This is a common problem in demand and supply models.

Missing relevant covariates The exclusion of a relevant covariate leads to the eﬀect being transferred to the residual instead. This causes endogeneity, since the residual is correlated with one (or more) of the previously included covariates. Hence, it is highly important to select as many compatible covariates as possible, before performing the regression.

Sample selection bias Sample selection bias arises when the sample of data is not randomly selected. Consequently, the residual explains an attribute that is not considered in the regression model.

Measurement errors Measurement errors is the diﬀerence between the actual results and the measured ones. This causes endogeneity as the covariates are incorrect, resulting in making the independent variables stochastic. Subsequently, the independent variables become correlated with the residual. [Lang, 2016]

3.5.4 Normality Plots are useful to examine if residuals meet the normality assumption, explained in section Plots and tests are useful tools to evaluate if residuals in regression models meet the normality assumption explained under section Key assumptions. This thesis will use Quantile-quantile plots (Q-Q) to assess if residuals are normally distributed.

Quantile-Quantile plots

By plotting the quantiles of the two variables x and y, it is visible to see if the two variables come from an identical distribution. The plot will follow a straight line with slope 1 if they have identical distribution. Furthermore, it is possible to identify if y is a linear function of the predictor variable x, as the plotted values follow a straight line.

23 A good estimate of the regression model is essential for the Q-Q plot to be accurate. The Q-Q plot is also useful for identifying outliers, skewness, heavy tails and bimodality [Gnanadesikan & Wilk, 1968]. Since normality is a key assumption for the OLS, it is of extreme importance that the OLS-estimator produces valid estimates.

3.5.5 Autocorrelation and cross-correlation Autocorrelation implies that adjacent observations are correlated, meaning that the values at diﬀerent times are co-dependent. Autocorrelation is typically un- desirable, as it means that the computation of correlations between data points is done adequately.

The auto-correlation of a stochastic process is the correlation between values at different times. Thus the function contains two different points in time, t and s. Then, Xt is the output value by the process at time t. The definition of the autocorrelation between time t and s is then: E[(X − µ )(X − µ )] R(s, t) = t t s s (29) σtσs where µX and σX are stationary values of the mean and standard deviation of the process Xt.

The cross-correlation function is used to ﬁnd the lag where the overlap between two functions is the greatest. The function is as follows:

E[(Xt − µX )(Yt+τ − µY )] ρXY (τ) = (30) σX σY where the values µX and σX are same values as in the equation above. The process Yt has the same characteristics as Xt.

The sample cross covariance function is a calculation of the covariance between two different time series, xt and yt at the different lags k = 0, ±1, ±2, .... This calculation is done by estimating the cross covariance at the different lags using: ( 1 PT −k(x − x¯)(y − x¯), k = 0, 1, 2, ... c (k) = T t=1 t t+k (31) xy 1 PT −k T t=1 (yt − y¯)(xt+k − x¯), k = 0, −1, −2, ... wherex ¯ andy ¯ are the sample means of the time series. The sample cross- correlation is now obtained from equation (31) by dividing with the square root of the sample variances,

cxy(k) rxy(k) = p p , k = 0, ±1, ±2... (32) cxx(0) cyy(0)

24 Durbin-Watson test

Durbin-Watson is a commonly used method to test for autocorrelation. The test statistics is as follows:

PT (e − e )2 d = t=2 t t−1 , (33) PT 2 t=1 et In the formula above,t is the time of the observation, while T is the number of observations. et is the residual of the observation at time t. The parameter d ranges between [0, 4], where a value d = 2 entails no autocorrelation. When d lies between zero and one, it implies a positive autocorrelation. Meanwhile, a value between three and four suggests a negative autocorrelation. In general, a d-value > 2 could result in an underestimation of the relevance of a covariate. [Durbin & Watson, 1951].

3.5.6 Spurious regression Imagine a scenario where the regression of y on x proves to be a significant relationship. However, after introducing another dependent variable z, the partial effect of x on y diminishes to zero. This is the so-called spurious regression, which is a term that describes a scenario where two variables are correlated through a third variable. To exemplify this, the following simple regression is used: ˆ ˆ yˆt = β0 + β1xt (34) ˆ which outputs an acceptable value of R-squared and t statistic for β1. However, Granger and Newbold [1974] proved through simulation that even though xt and yt are independent, the regression of yt on xt outputs a significant t-statistic a majority of the time, that is a lot higher than the nominal significance level. Hence, they named this the spurious regression problem, where there is no sense in the relationship between y and x, despite an OLS regression indicating the relationship. [Woolridge, 2009]

In statistics, a unit root is a phenomenon within stochastic processes. It can cause statistical interference in time series models. Also, it is a method of identifying a case of spurious regression. A unit root value of 1 implies that the linear stochastic process is the root of the process’ characteristic function. If a unit root exists, then the process is a non-stationary time series. There are various tests to ﬁnd a unit root, and in this thesis the Dickey-Fuller test was used. [Woolridge, 2009]

The Dickey-Fuller test examines two hypotheses. H0 is that the stochastic process has a unit root, while H1 states that the process is stationary. Consider the autoregressive model:

∆yt = (θ − 1)yt−1 + t = πyt−1 + t (35)

25 where yt is the independent variable, t is the time, θ is a coeﬃcient and is the error term. A unit root is present if θ is equal to one, or in the latter stage of the expression if π is equal to zero. This is as π = θ - 1. When π is less than zero, it is a stable autoregressive process, which implies that is asymptotically uncorrelated or weakly dependent. A value of π greater than zero is uncommon, as it means that the process is explosive. Thus, the method tests

H0: π = 0 against H1: π < 0

The Dickey-Fuller test then checks the t-test of H0, i.e.

θˆ − 1 πˆ τˆ = = (36) s.e.(θˆ) s.e.(ˆπ)

It is worth noting that the distribution only holds if the errors t are independent and identically distributed random variables. [Woolridge, 2009]

26 4 Method

This section will thoroughly describe the method used to study the problem and answer the research questions of the thesis.

4.1 Data Collection The data used to examine the relationship between the nominal exchange rate and commodity prices has been obtained from The Federal Reserve Bank of St. Louis’ database, FRED, the Bank for International Settlements, and Thomson Reuters Eikon. They consist of daily market closing price values. Spot prices were used for the commodities. The commodity prices and the nominal exchange rate extend from January 2nd 2009 to December 30th 2016, excluding weekends and on days when the market was closed, totaling a number of 2086 observations. Figure 1 below shows a plot of all of the data. Data for earlier periods of time were not found for all the commodities.

Exchange rate and Commodity indices 3 USDAUD Gold 2.5 Crude oil Natural Gas Iron

1.5

0.5

0 2009 2010 2011 2012 2013 2014 2015 2016 2017 Date

Figure 1: Plots of the AUDUSD exchange rate and the exported commodities. The curves show the USD price per relevant unit of each data series (see appendix for units), scaled by the ﬁrst value of the data series. That is, all series are divided by their value at 2016-01-02, the start of the data series. Some of the major economic events that occured during the period of data can be found in table 22. Note that the exchange rate is usually quoted as AUDUSD, meaning the AUD price of 1 USD. Inverting this value gives the USD price of 1 AUD and this is what is shown in the graph.

27 4.2 Literature Study Prior to writing the theoretical sections Theoretical Background and Mathemat- ical Theory, a comprehensive examination of the literature was conducted. A deeper understanding within the economical background was attained by using key words such as ”commodity currency”, ”real exchange rate”, ”purchasing power parity”, ”Dutch disease”, ”econometrics” and ”time series regression” when searching for previous studies and relevant literature. Google Scholar and KTH library’s search function were used to ﬁnd previous research within the topic. To ensure validity of our sources, only well-cited and peer-reviewed sources were selected. Also, primary sources were always preferred. Addi- tionally, Krugman’s and Well’s Economics [2013] was used as support for the macroeconomic theory.

Harald Lang’s Elements of Regression Analysis was used as base for the mathematical theory, together with literature from the class in regression analysis (both KTH and NUS) and Introductory Econometrics - A Modern Approach by Jeﬀrey Woolridge.

4.3 Choice of Country Before choosing the country of study, some selection criterias were developed. The country must be a primary commodity producer, were primary means raw or minimally processed material, with commodity export constituting a large share of the total GDP. The country also needs to be an industrialized economy and an active participant in the global commodity markets. In addition, the country must have had a floating exchange rate regime, preferably for a longer period of time. Lastly, the currency of the country must be heavily traded against the USD, as a highly liquid and stable foreign exchange market is central for a short-term trading strategy. A country that satisfies these criteria is a good candidate for a commodity based foreign exchange trading strategy, as the effect of other non-economic variables on the export and exchange rate are minimized.

Australia is such a country, with primary commodities constituting more than 60% of total exports [OEC, 2015], as it is one of the largest exporters among the industrialized nations [CIA, 2017]. The four chosen commodities (gold, crude oil, natural gas and iron) all constitute a large share of Australia’s total commodity export. Despite being a large producer, Australia still holds only a small share of the global commodity export. This also holds true for other commodity exporting nations due to the large number of producers on the market for many of the world’s most heavily traded commodities. The world’s commodity producers are all price takers, meaning that domestic events aﬀecting commodity production, generally, do not impact world markets. Some domestic events might be driven by global macroeconomic events, but these aﬀect other producers and consequently global markets. Furthermore, some producers form

28 organizations, of which the most famous is OPEC [OPEC, 2017], in order to co- ordinate commodity production to the beneﬁt of the producers. However, commodity producing countries generally do not hold the power to single-handedly alter global prices, and this holds true for the Australian commodity export. Furthermore, Australia has had ﬂoating exchange rates ever since the collapse of the Bretton Woods system in the 1970s, with limited central bank intervention under the period of study [RBA, 2017].

The mathematical consequence of the factors mentioned in the previous section is that changes in the global commodity prices are exogeneous to the AUDUSD exchange rate. That is, changes in global commodity prices are not caused by the Australian economy, for which the AUDUSD serves as proxy for. However, how the AUDUSD is aﬀected by changes in global commodity prices is exactly the problem under study in this thesis.

4.4 The Regression Model The aim of the research project is to study if there is a consistent and traceable relationship in daily movements of exchange rates and commodity prices. As mentioned earlier, commodity prices are exogenous to changes in the AUDUSD and it is possible that changes in commodity prices aﬀect the exchange rate, even on a daily basis. Fluctuations in commodity prices may produce, for example speculators to detect a rise in the commodity prices and take a position in the exchange rate based on this. As the time aspect of the mechanism is not known, the relationship at diﬀerent lags in time was also studied, to allow for a delayed impact from the commodity on the exchange rate.

The ﬁrst regression model is given in equation (37) and consists of the logarithm of returns on the AUDUSD, regressed on the daily changes in commodity prices, X log(yt/yt−1) = β0 + βi · (xi,t − xi,t−1) + t (37) i where yt is the AUDUSD exchange rate at time t, xi,t is the price of commodity i at time t and t is the error term. Studying the logarithm of the returns is a ubiquitous approach in mathematical ﬁnance, partly due to the variance- stabilizing properties of the logarithm.

Using the logarithm also allows for modelling nonlinear relationships between the dependent variable and the covariates. Furthermore, financial time series often exhibit autoregressive behaviour, and unless the series are properly differenced, results from regressions might be invalid. Newbold and Granger [1974] illuminated in their influential paper the potential pitfalls of spurious correlation and regression using time series integrated of order 1 or higher. A few years later, Engle and Granger developed the concept of cointegration, which ”makes regressions involving I(1) variables potentially meaningful” [Woolridge, 2009,

29 p.646]. Brieﬂy, cointegration implies that correlation between two time series is not spurious, instead there is a relation (also known as Granger causality) between the two. For example, two random walks can show high correlation without any real underlying relationship between the two. Newbold and Granger [1974] showed that standard test in regression does not apply when unit root processes are involved. The thesis intends to study if the exchange rate and the commodities are cointegrated, following the analysis by Cashin et al. [2003], by forming a weighted index of the commodities with weights based on their share of the export, i.e. the index CI at time t is given by

1 X CI = w P (38) t CI i i,t t=1 i where Pi is the price of commodity i at time t and wi is the weight, with P i wi = 1.

Then, the Engle-Granger two-step approachwas used to study cointegration between the two series, in which stationarity of the residuals of a regression with the level exchange rate and commodity series are investigated. If the two series are not cointegrated, a regression between them is spurious and gives no meaningful information about a relationship between the two. It is still possible to run a regression with the returns series, keeping in mind that this regression explains the returns in the exchange rate series based on the diﬀerences of the commodity series. However, these results have nothing to do with a relationship in levels [Woolridge, 2009].

The four commodities used are gold, crude oil, natural gas and iron ore. The model examines yearly periods over the data set, i.e. 2009-01-02 to 2009-12- 30 and similarly all the way up to 2016-12-30, partitioning the data into eight periods. It might be that the relationship between daily fluctuations in commodity prices and exchange rates varies from year to year from an economic perspective. A regression over the whole data set would make such an analysis impossible. Also, the exchange rate data consists of the nominal exchange rate, and so effects of inflation differentials on supply and demand are not accounted for. This is, however, not a problem when studying the partitioned data as effects of inflation are small over for each year. Furthermore, the relation between fluctuations is probably also affected by other global and domestic macroeconomic events and over an eight year period, many of such events may occur, as table 22 shows. From a mathematical perspective, partitioning might mitigate potential heteroscedasticity in the data, as different subgroups in the data should be more visible. Also, given the small number of covariates, the number of data points is believed to be roughly sufficient with yearly partitions.

30 The regression model with lagged covariates, i.e. the change in price at ki, where ki is the lag for covariate i, is given in equation (39) below, with the same notation as earlier. X log(yt/yt−1) = β0 + βi · (xi,t+ki − xi,t+ki−1) + t (39) i

4.5 Outline A brief summary of the steps performed in the analysis is as follows. First, each of the time series were studied separately for unit root behaviour. If evidence for unit roots is found, then the form of regression equation (37) is warranted, as discussed above. Then, the Engle-Granger two-step approach was used to examine the two series for a cointegrating relationship. Previous research in the field has studied cointegration between commodities and exchange rates (see [Cashin et al. , 2003] and [Chen & Rogoff, 2002] and references therein). How- ever, all of these studies used monthly real effective exchange rates as the dependent variable. The data used in this thesis consists of daily nominal exchange rates. If there is evidence suggesting cointegration, then these results corrob- orate previous research but also suggests that the relation between exchange rates and commodities is discernible on a shorter time scale than previously studied.

After the cointegration analysis, the regression model in equation (37) was studied for each partition of the data. As the model in equation (37) gives no information regarding the predictability of exchange rate fluctuations based on earlier movements in the commodities, equation (39) was studied at different lags to investigate if there appears to be a consistent, but delayed, relationship between the two. Appropriate lags were found by studying cross-correlations between the logarithm of returns of the exchange rate and the differenced commodity series. These results are also further supplemented by results from studying the similarity measure given in equation (11).

The potential benefits of using smoothed data in the regression model in equation (37) was also studied. The idea is that patterns might be difficult to detect on a daily basis, but more pronounced when the daily variations are smoothed. For example, if the average return over the past three days of a commodity is positive, it might produce a larger and consequently more discernible effect on the exchange rate. The smoothing was performed using two different weighting methods. One method used equally weighted moving averages, with weights given by the inverse of the window length. The other used non-uniform weights with larger weight given to more recent observations according to the equation

L X wi = i/ j, i = 1,. . . ,L (40) j=1

31 where L is the window length and wL is the weight for the most recent observation. The same analysis of lag, as for the unsmoothed data, was also performed for the smoothed data. All of these models were compared and analyzed.

Unlike for the models with lag, the regression in equation (37) can not be used to make predictions about future returns for the exchange rate, at least not without a price model for each of the commodity series. Simple autoregressive models are ﬁtted to each of the commodity series and predictions for each of these series are then used in the full regression equation to generate predictions of the next day exchange rate return. The predictive performance and the trading potential of the diﬀerent commodity based models was then be compared to a simple autoregressive model for the exchange rate.

32 5 Results 5.1 Preliminary analysis of the data and unit root analysis Figure 1 shows a plot of the full data set over the entire time span. Figure 2 and 3 below show the data for two of the yearly partitions, 2010 and 2014. Plots for the other years can be found in the appendix. These two periods are presented and studied in the following because they achieved the best and worst model ﬁt respectively. See appendix for similar analysis on the other years.

Exchange rate and Commodity indices 1.6 USDAUD Gold 1.4 Crude oil Natural Gas Iron

1.2

0.8

0.6

0.4 Jan 2010 Mar 2010 May 2010 Jul 2010 Sep 2010 Nov 2010 Jan 2011 Date

Figure 2: Plots of the data during 2010, the second partition of the data. Note that all series are indices, created by dividing the series with their value for the ﬁrst point in the partition, which in this case is the value at 2010-01-02. Iron ore prices hit all time high as disruptions in supply from India tightened the market. India is the third largest exporter of iron ore. Overall, the iron ore market saw a resurgence in production and higher demand from most countries after the stimuli packages from 2009 started to give eﬀect [OECD, 2011]. Gold prices continued to rise amid economic uncertainty, currency market unpredictability and the possibility of the US government buying back bonds. [Smith, 2010]

There are no clear trends in any of the time series when studying the yearly partitioned data, compared to figure 1 with the whole data set. The striking feature in figure 2 is how similar the movements of crude oil and AUDUSD appear to be. Also, gold and AUDUSD have similar movements. Figure 3 shows similar results, although with a stronger similarity between gold and AUDUSD, while it is weaker between crude oil and AUDUSD. The price of natural gas appears to have been unstable for roughly the first two months of the year.

33 Exchange rate and Commodity indices 2

USDAUD 1.8 Gold Crude oil Natural Gas 1.6 Iron

1.4

1.2

0.8

0.6

0.4 Jan 2014 Mar 2014 May 2014 Jul 2014 Sep 2014 Nov 2014 Jan 2015 Date

Figure 3: Same as in figure 2, but for 2014. Note that the series in this figure are scaled by their respective values at 2014-01-02. A cold 2013-2014 winter and record-high storage withdrawals led to high demand and a five year price spike in February for natural gas. Prices remained high during the spring but dropped in the summer due to strong production and inventory rebuilds. Iron ore prices slumped in 2014 as China’s economy slowed down and the world’s top miners ramped up production. Crude oil prices fell sharply in the last quarter as production exceeded demand, resulting in prices falling below the five-year average. [Lannin, 2014] [Teller, 2015]

To study if the time series used in the regression are unit root processes, an informal analysis of the autocorrelation (AC) of the level series and the differenced series are studied, together with the more formal Dickey-Fuller test. If the time series has a unit root, then the AC should show a very slow decay as a function of the lag. Figure 9 in the appendix shows graphs of the AC of the original time series in the left column and AC of the differenced time series in the right column. The slow decay in all plots in the left column is expected for an autoregressive process. After differencing the series there is virtually no AC left in the series, which indicates that the series could be described well by autoregressive processes of order one. The blue lines are confidence bounds for the AC of a completely random series, i.e. with no AC.

34 A Dickey-Fuller test was also conducted for each time series, where the null hypothesis is that the process has a unit root against the alternative of the series being stationary. Each test gave a very high p-value, with the smallest being 0.54 for natural gas, which should be interpreted as the data giving very little evidence against the null hypothesis. This is further indication that the time series under study exhibit unit root behaviour.

5.2 Cointegration analysis Following the approach used by Cashin et al. [2003], a weighted commodity index was created, consisting of the USD price of the four commodities weighted by their share of the commodity. Following this, the Engle-Granger two-step method was used to test for cointegration. xt represents the commodity index and yt is the original exchange rate series, indexed using its ﬁrst value. If xt and yt are non-stationary and cointegrated, a combination of them must be stationary. Letting β be the cointegration parameter, it is written as:

yt − βxt = ut (41) where ut is a stationary process. As the cointegration parameter β and ut are not known, they are estimated using the following regression:

yt = α + γxt + et (42)

An estimate for the cointegration parameter β is now given by the estimate of γ, γˆ, and an estimate foru ˆt−1 is given by the residuale ˆt. Now, the estimated series can be tested for stationarity using the Dickey-Fuller test, in which a second regression is run using the estimated series, i.e. ∆ˆut is regressed onu ˆt and the t-statistic for the coeﬃcient onu ˆt is studied using the critical values in table 1.

Signiﬁcance level 1% 2.5% 5% 10% Critical value -3.90 -3.59 -3.34 -3.04

Table 1: Asymptotic critical values for cointegration test in the Engle-Granger two-step method. [Woolridge, 2009, p.647]

Values for the t-test, for each year, can be found in the table 2 below.

Year 2009 2010 2011 2012 2013 2014 2015 2016 β 0.8285 0.6984 1.0390 1.4616 0.3269 1.3492 0.6600 1.2976 t-stat -3.04 -2.46 -2.15 -2.12 -1.96 -3.02 -2.09 -1.92

Table 2: Table with estimated value for the cointegration parameter β and the corresponding t-stat, for each year. The t-stat are compared to the critical values in table 1.

35 The values for the t-statistics are compared with the critical values in table 1, to determine the level of significance. None of the t-stats are significant on a 10% level, which shows little evidence for rejecting the null hypothesis of no cointegration. Different lags of the residual series were also used in the Dickey-Fuller test, to study if there is cointegration at any lags between the exchange rate and the commodity index. Lags up to 15 days were used but none of these were significant at a 10% level, further indicating that the two series do not appear to be cointegrated. Note that equation (41) does not allow for structural breaks, i.e. subpopulations with different properties in the series. The partition of data, however, is believed to mitigate the effect of such breaks, motivating the use of equation (41).

5.3 Regressions without lag The results from the previous section indicate that there is no cointegration between the level of the commodities and the exchange rate. This further war- rants the form of the regression model in equation (37), as discussed in earlier sections. Equation (37) also allows us to study the specific effect of each of the four commodities on the exchange rate. The results from the regressions for 2010 and 2014 can be found in table 4 and 5 below. Results for the other years can be found in the appendix. Scatterplots for the data in these two regressions can be found in the appendix (figure 4 and 5) and the variance inflation factor for each covariate are given in table 3 below. The low VIF values indicate that the covariates have a low degree of correlation between each other, ensuring that the inflation of the OLS estimates is small.

2010 and 2014 are the years with the best and worst fit respectively and plots of the data for these years can be found in figures 2 and 3 above. Not surprisingly, crude oil series explains a lot of the variation in the exchange rate, indicated by the magnitude of the coefficient and large t-stat. Gold also appears to be important in the model, while natural gas and iron could possibly be removed without reducing the fit of the model. The small t-statistic for iron is somewhat surprising, as iron is one of Australia’s largest export, constituting roughly 20% of the total export in 2015 [OEC, 2015]. The sign for gold and crude oil is rea- sonable, as higher prices for the commodities should benefit the producer. The positive sign indicates that AUD becomes more expensive, in terms of USD, when the price of gold and crude oil does.

Gold Crude oil Natural gas Iron 2010 1.0621 1.0789 1.0158 1.0089 2014 1.0213 1.0059 1.0102 1.0095

Table 3: Variance inﬂation factor for the two regression models, calculated according to equation (27).

The regression for 2014 shows similar results as for 2010 for all commodities

36 Coefficients Estimate SE tStat pValue ______Intercept 7.3236e-05 0.00041305 0.17731 0.85941 Gold 0.098894 0.037176 2.6602 0.008305 Croil 0.2738 0.02463 11.116 1.1409e-23 NG -0.014141 0.01617 -0.87453 0.38265 Iron 0.030313 0.027548 1.1004 0.27221

Number of observations: 260, Error degrees of freedom: 255 Root Mean Squared Error: 0.00658 R-squared: 0.382, Adjusted R-Squared 0.372 F-statistic vs. constant model: 39.4, p-value = 1.07e-25

Table 4: Results from the regression using equation (37) for the year 2010. Note that the differenced series are used for the covariates and the logarithm of the returns are used for the dependent variable. As the series are indices, all coefficients are unitless. except crude oil, which now appears to be of no use in the model. This a striking difference compared to the model for 2010, where crude oil had a very large t-statistic. The regression also shows a worse fit compared to 2010, with lower R2 and adjusted R2 values. Comparing these results with regression results for the other years, the conclusion is that natural gas and iron generally explain very little of the variation in the exchange rate. The t-statistic for these commodities all have large p-values for each year, with the exception of 2016 where the t-statistic for iron had a p-value of 0.035. Although rigorous analysis, for example using F-tests and the AIC, is necessary before any final conclusions can be drawn, the results indicate that only gold and crude oil prices affect the daily returns for the exchange rate, for the year under study. The intercept appears to be insignificant in both regressions. Removing the intercept imposes strict assumptions of the dynamic of the relationships between the dependent variable and covariates. Specifically, it signifies that the mean of the dependent variable is zero when the covariates are zero, which might not be true. Therefore, it is kept in the model as given its small value in both regressions, it has a negligible effect on the dependent variable.

Further analysis and testing of this model is postponed until later sections and the regressions with lagged variables are studied in the following.

37 Coefficients Estimate SE tStat pValue ______Intercept -0.00022123 0.00030547 -0.72422 0.46959 Gold 0.11032 0.037114 2.9725 0.0032363 Croil 0.032482 0.033505 0.96947 0.33323 NG -0.0053388 0.0035708 -1.4951 0.13612 Iron 0.032003 0.028439 1.1253 0.26152

Number of observations: 260, Error degrees of freedom: 255 Root Mean Squared Error: 0.00474 R-squared: 0.0503, Adjusted R-Squared 0.0354 F-statistic vs. constant model: 3.38, p-value = 0.0103

Table 5: Results from the regression using equation (37) for the year 2014. Note that since the covariates are indices, with different scales for each year, the coefficients need to be re-scaled before comparison can be made between different years, as the OLS is not scaling invariant.

5.4 Regressions with lag Plots of the sample cross-correlation for 2010 and 2014 can be found in figures 4 and 5. The correlations at lag = 0 for each commodity is in correspondence with the results from the regressions in the previous sections. The noticeable lags for 2010 data, are at around -12 for gold, +15 for crude oil and around -3 and 20 for iron (in days). For the 2014 data, noteworthy lags are at +7 for gold, around -5 for crude oil, +10 for natural gas and possibly +20 for iron. These values were also compared to the ones obtained from the similarity measure in equation (11). A table of the values of equation (11) for each commodity at different lags can be found in table 23 in the appendix. Regressions were run using different lags for each commodity, at the best lags found in the analysis. That is, the logarithm of the exchange rate was regressed on the commodity series, where different combinations of lags where included for each commodity. Note that the only restriction was that two adjacent lags, for a commodity, could not be used in the same regression as the two covariates would be perfectly correlated.

The same analysis was performed for each year, using the optimal lags found for that year. The best model, over all years and combinations, is given in table 6. The t-stat for all coefficients are very small, not to mention the F-statistic versus a constant model and the negative adjusted R2. The other regressions are not presented here as they all had very large F-statistics versus a constant model, with only an intercept, and values below 1% for R2 and even negative values for the adjusted R2. These results suggest that model with lags included, even when the lag is only 1, hold little information about the next day’s exchange rate. Different functional forms for the regression equation were also used, with quadratic and interaction terms for the covariates and relative returns, defined

38 as (yt−yt−1) , for the dependent variable. None of these models oﬀered a better yt−1 ﬁt, compared to the model in 6, after controlling for irrelevant terms. Hence, further analysis was not necessary.

Gold Crude Oil 0.4 0.6

0.4 0.2 0.2 0 0

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag Lag Natural Gas Iron 0.2 0.2

0.1 0.1

0 0

-0.1 -0.1

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag Lag

Figure 4: Plots of the cross-correlation between the logarithm of the exchange rate return and the four diﬀerent commodities, where the correlation positive and negative lags are calculated according to equation (32). Data is for 2010.

Coefficients Estimate SE tStat pValue ______Intercept 0.00038979 0.00053776 0.72484 0.46924 Gold, lag 1 -0.0028812 0.047925 -0.06012 0.95211 Gold, lag 3 -0.0099578 0.031697 -0.31415 0.75367 Croil, lag 2 0.018807 0.023317 0.80657 0.42069 Croil, lag 4 0.035385 0.0353 1.0024 0.31712 Croil, lag 7 -0.085277 0.047845 -1.7824 0.07592 Ngas, lag 2 0.025501 0.031754 0.80309 0.4227 Iron, lag 8 -0.0091222 0.02081 -0.43835 0.66151

Number of observations: 254, Error degrees of freedom: 246 Root Mean Squared Error: 0.0084 R-squared: 0.0199, Adjusted R-Squared -0.00799 F-statistic vs. constant model: 0.714, p-value = 0.661

Table 6: Table showing the regression output for the optimal model found with lags, for 2010. Note that all commodity series are diﬀerenced.

39 5.4.1 Smoothed data To study if daily variations in data obscured potential long-term trends, where long-term in this sense is more than two days and shorter than a month, smoothed versions of the data were created. The smoothed data was obtained using moving averages, as described in the method, of different lengths up to a maximum of 15 days, corresponding to three business weeks. For each value of the moving average window, the same analysis as performed above for the models without lag was conducted for each year, according to equation (37). Different combinations of lags, found by studying plots of the sample autocorrelation and the similarity measure, were also experimented with in the regressions, according to equation (39). The smaller number of observations in these regressions compared to the ones in the models without lags is due to the removed initial values for the series. The simple moving average weights each observation equally, with weights given by the inverse of the window length. Hence, the first points in the series, up to the size of the window length, were removed.

The emerging trend from the analysis was that the fit of the model generally followed a U-shaped function of increasing window length, as table 8 shows. For the models without lag, the fit showed an initial large reduction for small degrees of smoothing with a slight improvement with increasing window length. This is somewhat surprising as longer periods of positive trends for the commodity series is believed to produce periods of positive trends for the exchange rate, keeping all other factors fixed. None of the best models with smoothing and without lag offered improvements, compared to their non-smoothed counterparts. The best model, in the sense that it had the highest value for the F-statistic versus a constant model, R2, adjusted R2, over all years and smoothing lengths are given in table 7.

The smoothing did not improve the models with lagged covariates, studied in the previous section, either. Special care was necessary when using lags together with smoothing, as lagged covariates of the same commodity become more correlated with increasing window length. This multicollinearity can be tolerated as it is artificially introduced to the data, even though it inflates the variance estimates of the OLS coefficients. However, none of the models with smoothing and lags showed a better model fit compared to the smoothed model without lag and were therefore not further analyzed.

40 Coefficients Estimate SE tStat pValue ______Intercept 0.00037897 0.00052307 0.72451 0.46943 Gold -0.49716 0.36928 -1.3463 0.17942 Croil 1.0667 0.21004 5.0785 7.4234e-07 Ngas 0.091905 0.16116 0.57029 0.56899 Iron -0.015212 0.1509 -0.10081 0.91979

Number of observations: 256, Error degrees of freedom: 251 Root Mean Squared Error: 0.00797 R-squared: 0.103, Adjusted R-Squared 0.0886 F-statistic vs. constant model: 7.19, p-value = 1.69e-05

Table 7: Table showing the regression output for the smoothed covariates, with no lag and a smoothing window of 5 days, for 2010. Note that all commodity series are diﬀerenced.

Smooth 2 3 4 5 10 15 R2 0.0118 0.00663 0.0156 0.0244 0.0277 0.0255 adj. R2 -0.00376 -0.00907 -4.68e-06 0.00883 0.0118 0.00928 F-stat 0.758 0.422 1 1.57 1.75 1.57 p-value 0.553 0.792 0.408 0.184 0.141 0.183

Table 8: Table showing diﬀerent regression statistics for the models with smoothed data and no lags, for the year 2010. The F-statistic is versus a constant model. The values in the row named ”Smooth” indicates the length of the window used in the smoothing.

41 Gold Crude Oil 0.2 0.2

0.1 0.1

0 0

-0.1 -0.1

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag Lag Natural Gas Iron 0.2 0.2

0.1 0.1

0 0

-0.1 -0.1

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag Lag

Figure 5: Same as in ﬁgure 4, but for 2014.

5.5 Analysis of models The results in the earlier sections indicate that including lags in the regression models does not add much explaining power, with the best model found given in table 6. The low F-statistic and the negative adjusted R2 value indicate that these model are not preferable over a model with only an intercept. Similarly, analysis of smoothing in the previous section showed that using smoothed covariates in the regression did not improve the model ﬁt. Therefore, these models are not further analyzed and attention is instead focused on the models for 2010 and 2014, without lag and smoothing. These models are given in table 4 and 5. It should be noted that the model ﬁt measured by the R2 and the adjusted R2 does not imply good predictive properties for the model out of sample, which is the important aspect in a model based trading strategy. Hence, the model for 2014, could still generate good predictive performance. Here, a deeper analysis is made of the validity of the OLS assumptions and the properties of the regression model.

Model selection As noted earlier in the result section, the coefficients for natural gas and iron do not appear to be significant in the model for 2010. An F-test for the restricted model in table 9 against the full model has a p-value of 0.56424, indicating that the null hypothesis can not be rejected and that natural gas and iron are jointly insignificant in the model. The AIC for the full model is −1.8694 · 103 and the model without natural gas and iron −1.8713·103, which further corroborates the

42 result from the F-test. Furthermore, the equal values for the adjusted R2, the diﬀerence is less than 10−3, suggests that the two commodities can be removed from the model. Coefficients Estimate SE tStat pValue ______Intercept 0.00014173 0.00041006 0.34563 0.7299 Gold 0.098564 0.037137 2.6541 0.0084482 Croil 0.27375 0.024412 11.214 5.089e-24

Number of observations: 260, Error degrees of freedom: 257 Root Mean Squared Error: 0.00658 R-squared: 0.377, Adjusted R-Squared 0.372 F-statistic vs. constant model: 77.9, p-value = 3.66e-27

Table 9: Regression for 2010, without natural gas and iron. Note that neither of the two became signiﬁcant in the model, after removing natural gas and iron.

For 2014, natural gas and iron again appear to be of little use in the regression model. The F-statistic for the restricted model without the two is 1.73822 and corresponds to a p-value of 0.82208, indicating again that natural gas and iron are jointly insigniﬁcant in the model. The AIC gives the same result. Both of them are therefore dropped and regression results for the restricted model is given in table 10 below.

Coefficients Estimate SE tStat pValue ______Intercept -0.0002785 0.00030186 -0.92261 0.35708 Gold 0.10947 0.036905 2.9663 0.0032981 Croil 0.029939 0.033569 0.89185 0.37331

Number of observations: 260, Error degrees of freedom: 257 Root Mean Squared Error: 0.00476 R-squared: 0.0373, Adjusted R-Squared 0.0298 F-statistic vs. constant model: 4.98, p-value = 0.00753

Table 10: Regression for 2014, without natural gas and iron.

The difference between this restricted model for 2014 and the same model for 2010 is that crude oil is non-significant, even at a 37% level, compared to the result in table 9. To investigate if crude oil should be in the model, the F- statistic is calculated for the full model versus the restricted model with gold as the only covariate. The F-statistic is 1.42443, with a p-value of 0.76391, suggesting that the three covariates are jointly insignificant for 2014. The AIC is also minimized for this model, taking the values −2.03959·103, −2.04006·103 and −2.04125·103 for the full, restricted and model with only gold, respectively. Residual analysis

43 Coefficients Estimate SE tStat pValue ______Intercept -0.00033516 0.00029498 -1.1362 0.25693 Gold 0.11154 0.036818 3.0294 0.0026989

Number of observations: 260, Error degrees of freedom: 258 Root Mean Squared Error: 0.00476 R-squared: 0.0343, Adjusted R-Squared 0.0306 F-statistic vs. constant model: 9.18, p-value = 0.0027

Table 11: Regression for 2014, without natural gas, iron and crude oil.

Plots of the residuals for the 2010 model in table 9 are shown in ﬁgure 6 in the next page. The left plot shows that the residuals appear to follow a white noise process, with no particular trends or autoregressive behaviour. The second graph, the Quantile-Quantile plot, shows that the residuals could be closely approximated with a normal distribution, given the close similarity between the quantiles. A Durbin-Watson test was also used to test the residuals for autocorrelation, with a Durbin-Watson statistic of 1.9927 and a p-value of 0.6534. The null hypothesis for the test is that the residuals are serially uncorrelated, against the alternative of the residuals following an autoregressive process of order 1, with the large p-value reported oﬀering very little evidence against the null hypothesis.

Plots of the residuals for the 2014 model can be found in figure 24 in the appendix. The normality approximation appears to be slightly worse for this model, with more pronounced deviations in the QQ-plot compared to the one in figure 6. In particular, the residuals appear to follow a distribution with heavier tails compared to the normal distribution, which is common for returns in financial times series. The Durbin-Watson statistic for this model is 2.0237 with a p-value 0.9168, indicating that the residuals are not autocorrelated.

44 Normal Probability Plot 0.02 0.999 0.997 0.015 0.99 0.98 0.01 0.95

0.005 0.90

0 0.75

-0.005 0.50 Probability -0.01 0.25

-0.015 0.10

0.05 -0.02 0.02 0.01 -0.025 0.003

-0.03 0.001 Jan 2010 Apr 2010 Jul 2010 Oct 2010 Jan 2011 -0.02 -0.01 0 0.01 0.02 Data

Figure 6: The left plot shows the estimated residuals from the regression for 2010, plotted against time. The right graph shows a Quantile-Quantile plot of the residuals. Both plots show a potential outlier, around May.

Heteroscedasticity analysis

By partitioning the data into yearly periods, most of the heteroscedasticity was mitigated, which was veriﬁed by running the Breusch-Pagan test for regression model for the whole data set and comparing it to the yearly sets, which had much larger p-values compared to the whole data set. The null hypothesis for the test is that the data is homoscedastic. Estimates of White’s heteroscedastic consistent variance were also calculated and are shown in table 12, for the 2010 model. The values diﬀer from the original OLS variance estimates by a few percent at most and not enough to alter the conclusion from the t-tests, which is in accordance with the result from the Breusch-Pagan test. The same holds true for the 2014 model, where the two standard errors estimated using White’s method are 0.00031 and 0.03861, respectively.

Coefficients Estimate White’s SE tStat pValue ______Intercept 7.3236e-05 0.00042045 0.17418 0.85941 Gold 0.098894 0.038736 2.5530 0.008305 Croil 0.2738 0.02523 10.8521 1.0e-23

Number of observations: 260, Error degrees of freedom: 257 Root Mean Squared Error: 0.00658 R-squared: 0.382, Adjusted R-Squared 0.372 F-statistic vs. constant model: 39.4, p-value = 1.07e-25

Table 12: Results from the regression using equation (37) for the year 2010, with t-stat and the corresponding p-value calculated using White’s estimator.

45 5.6 Trading results As mentioned earlier in the method section, the regression model in equation 37 can not be used to predict returns for the exchange rate, without predictions for the commodity returns. The preliminary analysis of the data showed that the commodity series could be modelled using an autoregressive process of order 1, denoted as AR(1). Results from the ﬁtting of the commodity series in the model in table 12, to AR(1) processes using OLS can be found in table 13 below. As indicated in the earlier analysis, the φ-coeﬃcients are all close to one, meaning that the series exhibit unit root behaviour.

Parameter Value Standard Error t-statistic cg10 0.00529 0.00804 0.65820 φg10 0.99614 0.00712 138.54000 2 −6 σ g10 0.00013 9.12513·10 13.96860 cc10 0.01762 0.01591 1.10759 φc10 0.98331 0.01593 61.71760 2 −5 σ c10 0.00029 2.31508·10 12.68840

cg14 0.01720 0.01029 1.74604 φg14 0.98278 0.00990 99.32970 2 −5 −6 σ g14 6.34177·10 5.00218·10 12.67800

Table 13: Table showing parameter estimates for AR(1) processes ﬁtted to the commodity series in the table 4 and 5. The notation ”g” stands for ”gold”, ”c” for crude oil, ”10” for 2010 and ”14” for 2014. The rows with the σ2:s give the estimated variance for the zero-mean noise term in the AR(1) model.

The QQ-plots above showed that the residuals from the OLS regressions are approximately normally distributed. Assuming that this is the true distribution of the residuals, and assuming that zero-mean noise in the AR(1) processes also follow a gaussian distribution, the distribution for the next day exchange rate 2 returns can be derived. Speciﬁcally, if t ∼ N(0, σ ), then

2 Xt+1 = c + φXt + t ∼ N(c + φXt, σ ) (43)

2 Subtracting with Xt on both sides now gives Xt+1 − Xt ∼ N(c + Xt(φ − 1), σ ). By noting that the sum of normally distributed variables also is normally distributed with mean and variance given by the sum of the means and variances, the distribution for the logarithm of the exchange rate returns is given as follows yt+1 X 2 X 2 2 log ∼ N β0 + βi(ci + xi,t(φi − 1)), σ + β σ (44) y ε i i t i i where independence is assumed between the covariates in the calculation of the 2 variance. σε is the estimated variance for the residuals for the regression in table 2 12 and σ are the estimated variance for each AR(1) series for the covariates, given in table 13 above. This equation gives the distribution for yt+1, which is

46 the indexed exchange rate at time t + 1, after some simple algebra. Predictions and confidence bounds for the next day exchange rate can now be calculated using the mean and standard deviation of equation (44). Results for in-sample and out-of-sample prediction for the model in equation (12) can be found in figure 7 below. As a comparison, an AR(1) process was also fitted to the exchange rate series. Prediction results for one-day ahead predictions for the two models are shown in Figure 7.

Prediction

1.14

1.13

1.12

1.11

1.1

1.09

1.08

1.07

1.06

Dec 01, 2010 Dec 06, 2010 Dec 11, 2010 Dec 16, 2010 Dec 21, 2010 Dec 26, 2010 Dec 31, 2010 Jan 05, 2011 Jan 10, 2011 Jan 15, 2011 Jan 20, 2011 Jan 25, 2011 Jan 30, 2011

Figure 7: Plots of the predictions results for the commodity model and the AR(1) model for the exchange rates. At each day, the plot shows the prediction generated using data for the previous day for the commodity based model (red), predictions generated using data for the previous day for the AR(1) model for the exchange rate (blue) and the true exchange rate for that day (black). The dotted blue lines are the upper and lower 95% confidence bounds for the exchange rate AR(1) process. Confidence bounds for the commodity model are not visible in the figure, as they are much larger. Note that the blue curve is almost not visible behind the black curve. The figure shows in-sample prediction from 2010-12-01 up to 2010-12-30, the last data point used in the estimation of the regression model, and out-of-sample prediction for one month, ending in 2011-01-31.

The striking feature of the plot is how closely the simple AR(1) process for the exchange rate series appears to follow the true price dynamics. The table below shows the mean and variance of the relative errors for each prediction series. As Figure 7 indicates, the autoregressive model for the exchange rate series shows much better predictive performance compared to the commodity based model. This is the case for both the 2010 model and the 2014 model.

47 Model Mean Variance Commin,10 0.3269 0.5829 Commout,10 0.5514 0.8037 AR(1)F X,in,10 0.0207 0.5757 AR(1)F X,out,10 -0.2169 0.7908

Commin,14 0.3540 0.4056 Commout,14 0.3648 0.8315 AR(1)F X,in,14 0.1540 0.4043 AR(1)F X,out,14 0.1596 0.8169

Table 14: Table shows the mean and variance for the relative prediction error, given as percentages. Rows denoted with ”Comm” are for the commodity based model from equation (44). Subscript ”in” refer to the in-sample prediction and ”out” to the out-of-sample prediction.

Prediction

0.96

0.95

0.94

0.93

0.92

0.91

0.9

0.89

0.88

0.87

0.86

Dec 01, 2014 Dec 06, 2014 Dec 11, 2014 Dec 16, 2014 Dec 21, 2014 Dec 26, 2014 Dec 31, 2014 Jan 05, 2015 Jan 10, 2015 Jan 15, 2015 Jan 20, 2015 Jan 25, 2015 Jan 30, 2015

Figure 8: Plots of the predictions results for the commodity model and the AR(1) model for the exchange rates. The ﬁgure shows in-sample prediction from 2014- 12-01 up to 2014-12-30, the last data point used in the estimation of the regression model, and out-of-sample prediction for one month, ending in 2015-01-31. Note that performance for 2014 is comparable to the 2010 model, even though the 2014 model had smaller values for the goodness-of-ﬁt measures.

48 6 Discussion

The results from the cointegration analysis showed that there is very little evidence for cointegration, even for year 2010, which had the best model fit for all years studied. Lags of the residuals were also included in the Dickey-Fuller test to study a possible delayed cointegration, and again the results showed that there was little evidence for cointegration. This is in contrast to previous research in Cashin et al. [2003] and the results in Chen and Rogoff [2002], for which cointegration was found between the monthly REERs and commodity price indices for each of the commodity currencies studied. The period of study in this thesis was also different from the one studied the two papers cited above. Both were written in the early 2000s and used data from the late 1970s up to the early 2000s. The data studied in this thesis is from 2009-01-02 up to 2016-12-30 and the global markets and macroeconomic conditions have definitely changed, with the easiest example being the 2008 financial crisis. This could explain the different results obtained compared to previous research.

The commodity index used in the study of the cointegration was created using the four commodities weighted according to each commodity’s share of the total export in 2015. This commodity index was used on all of the years, and thus not adjusted to reflect potential changes in the share of the total export that the commodities might have had. This could be regarded as a potential source of error in the cointegration. However, large changes in a country’s export generally need a longer period of time to occur, as large-scale production facil- ities are usually run for decades. Also, the commodities studied are consumed in such a vast number of different ways that their total demand has probably not affected by technological development, during the period study in this thesis.

As mentioned earlier, the implication of no cointegration between two-time series is that a regression of one on the other is spurious and gives no meaningful information about the level relationship between the two. However, it does not rule out the possibility of there being a relationship between the differenced series. It might be that the level relationships between exchange rates and their commodities only exist on the long-term, where trading is probably driven by macroeconomic fundamentals such as PPP, inflation and interest rate differentials, global supply and demand, etc. It is possible that the mechanism that drives the relationship between the exchange rates and their respective export commodities needs some time to gain full effect, and therefore is not detectable on the shorter time scale studied in this thesis. For example, many major economic events that affect producers and investors occur at monthly or quarterly intervals. Also, producers and consumers generally do not alter the timing of large-scale transactions based on daily price fluctuations.

Daily price ﬂuctuations are probably mainly aﬀected by speculators, in contrast to large corporations and governments, moving in and out of positions with short duration. The fact that general high level of explaining power for all of

49 the models with the returns series and variables without lag seem to hold, might be an indication that speculators, at least partially, base their trading decisions on fluctuations in the respective commodity for the exchange rate. Furthermore, today’s electronic markets offer second-by-second trading, enabling speculators to rapidly respond to relevant new or price fluctuations in the commodities and exchange rates. It would be interesting to study the dynamics between exchange rates and commodities on a shorter time scale, to see if there is a strong relationship between levels on a shorter duration.

Another indication that the daily fluctuations could be mainly driven by speculators, are the varying estimates for the coefficients and the model fits. All of these regressions were run using the same regression model, equation (37), yet the results for different years differ greatly, as shown in the comparisons for the 2010 and 2014 data. Not surprisingly, global commodity markets were affected by very different events, with a world market recovering from the recession and seeing the first effects of the stimulus package in 2010, and generally declining commodity prices in 2014, with natural gas being especially volatile. Most speculators adapt their strategies to market conditions, which implies that trading strategies would look very different for different years. In other words, there is no trading strategy that suits all market conditions.

The most surprising result regarding the importance of the commodities in explaining variations in the exchange rate is the small, and almost always insignificant, estimate of the coefficient for iron. Iron ore export is one of Australia’s most exported commodity, almost as large as the other commodities studied combined. One explanation for this could be the distribution of the world consumption of iron. China is the world’s largest importer of iron ore, responsible for over half of the worlds iron ore import. Hence, the demand for iron ore from the Chinese market, and thus, the state of Chinese economic growth, is often reflected in the price of iron ore. Consequently, Australia’s iron ore export is likely highly correlated with the Chinese economy, although the AUDUSD might not be affected by it.

The results in the section about lags show that the models with lagged covariates are inferior to the models without lag, even when compared to a constant model with only an intercept. The implications of this is that all explaining power in the commodity series are concentrated into the daily ﬂuctuations of the two, with lags holding no further information. Somewhat surprisingly, the models with smoothed versions of the time series also showed no improvement compared to the models without lags. The implication is similar as for the models with non-smoothed data, with the addition that the relationships between the exchange rate and commodities become less detectable with higher degrees of smoothing, further adding to the hypothesis that the daily ﬂuctuations are mainly driven by speculators.

50 The poor fit for the model concerning year 2014 could possibly be explained by the volatile spot price for natural gas and crude oil. Natural gas prices are primarily determined as a function of supply and demand. As there are few short-term alternatives to natural gas, large price fluctuations can occur due to short-term shifts in demand. Since natural gas is used as a fuel for heating and electricity generation, weather changes have a major effect on demand, and thus the price. For instance, cold winters can have a big impact on the prices, while hot summers cause demand for cooling to increase, and therefore natural gas demand by electric power plants. Other factors affecting the demand side are economic conditions and petroleum prices. This is due to petroleum’s perk as an economical substitute for large building owners, power generators, and manufacturers [USEIA, 2013]. The year of 2014 started off coming from a record breaking cold winter, resulting in high demands and storage withdrawals, which was reflected in the prices. However, the strong demand was followed by record production and inventory refilling leading to a drop in price. Consequently, this influenced our regression negatively.

In the trading analysis, two types of models were compared: a model using information about commodities to predict exchange rates and a model, which essentially is a random walk, for the exchange rate series. To make predictions for the commodity series, AR(1) processes were fitted to each series, for lack of other short-term commodity models. The results show that the simple, and in a sense non-informative, AR(1) model outperforms the informative commodity model, with some margin. This in line with the most of the research in the field, beginning with Meese and Rogoff’s influential paper, where they showed that exchange rate models failed to outperform the random walk in out-of-sample predictions. This thesis shows that their conclusion also holds true for the daily data studied here. Even though the regression model somewhat limits the possible functional forms for the relation between the dependent variable and the covariates, it still offers an approximation of the true model. As such, the in- ability of the model used in this thesis to outperform the random walk is more likely a manifestation of the difficulty in modelling exchange rates, rather than a poor choice of regression model.

In an attempt to identify the Dutch disease in Australia, a first sign was the significant correlation between the four commodities and the Australian dollar. This itself does not prove the Dutch Disease, however, Australia has had an abundance of resources during the last decades which inspired the initial thoughts of the phenomenon. When looking at figure 1, there is an increase of iron, crude oil and gold prices during 2009-2014, while the currency also appre- ciated. According to the Dutch disease, the consequence should be a declining manufacturing sector. In 2014, the consequence was apparent, as Australia’s au- tomotive industry was dying. Major car manufacturers Ford, General Motors and Toyota closed down their factories in Australia, which they had operating for over 40 years [Dowling, 2017]. Ever since the commodity boom in Australia

51 from year 2000 onwards, the manufacturing sector has been slowly diminish- ing. Investments in the sector are fading, whilst the sector stands for a smaller portion of the country’s GDP. In addition, the labour costs within the sector has doubled since year 2000, which is the highest increase in the world. Con- clusively, there are a lot of signs indicating that the Dutch disease has struck Australia. [Langcake, 2016]

Summarizing the results, one main point is worth emphasizing. The instability of the coefficient estimates over time indicates that a trading strategy, focused on the USDAUD and the Australian exports, needs to be highly adaptable to current global macroeconomic events and factors affecting the consumers and producers of commodities, as these appears to highly variable over time. As the results from the regressions show, it is not enough to train a model on one year’s data and used this model for trading during the following year. It might be possible to update the model parameters adaptively, as the suggested model only describes the relation between exchange rates and their respective commodity currencies under current market conditions. However commodity markets are among the most volatile markets, making them potentially highly profitable but at the expense of a higher risk, and modelling of them should take this into account.

To conclude the discussion and answer the original research question, the cointegration analysis showed that there is little evidence for a short-term relationships existing between the level of the nominal USDAUD exchange rate and the commodity prices, but the data suggest that there could exist some relationship between the returns. The results also show that information about the commodity series oﬀers no improvement in predictive performance over a simple AR(1) model for the exchange rate, and the suggested model should therefore not be used in a short-term trading strategy for the exchange rate.

52 7 Further Research

More research regarding the mechanism behind how daily prices affect the exchange rates would be of interest. Current studies primarily focus on long-term effects, rather than short-term. Indeed, it could be that short-term fluctuations is mostly an effect of speculations but due to lack of research on the subject, conclusions are hard to draw.

Since this thesis only examined Australia, it would be of interest to study other countries considered to have so-called ”commodity currencies”, especially those that do not have the same commodities as Australia as their main source of export. Looking at developing countries that have an export that is mainly consisting of commodities more than 80% would also be of interest. They were not included in this thesis as these countries have issues with inflation, and thus their currencies would be more influenced by economic factors rather than commodity prices. It would furthermore be of interest to compare to countries that are not considered to be commodity exporters. Data over more commodity prices could also have helped to improve the models offer a comparison.

Regarding the trading strategy, further research would be recommended to look at shorter time spans, such as minute or second ﬂuctuations. Previous research has found cointegration during monthly movements, however, it would be groundbreaking if cointegration existed in shorter time spans.

53 8 References

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56 57 9 Appendices 9.1 Graphs

Gold Gold 1 1

0 0

-1 -1 0 5 10 15 20 0 5 10 15 20 Crude oil Crude oil 1 1

0 0

-1 -1 0 5 10 15 20 0 5 10 15 20 Natural gas Natural gas 1 1

0 0

-1 -1 0 5 10 15 20 0 5 10 15 20

Sample Autocorrelation Iron Sample Autocorrelation Iron 1 1

0 0

-1 -1 0 5 10 15 20 0 5 10 15 20 USDAUD USDAUD 1 1

0 0

-1 -1 0 5 10 15 20 0 5 10 15 20 Lag Lag

Figure 9: Plots of the sample autocorrelation for the original data in the left column and the diﬀerenced data in the right column. The blue lines are conﬁ- dence bounds for the autocorrelation of a completely random series, i.e. with no autocorrelation.

58 Exchange rate and Commodity indices 2 USDAUD 1.8 Gold Crude oil 1.6 Natural Gas Iron

1.4

1.2

0.8

0.6

0.4

0.2 Jan 2009 Mar 2009 May 2009 Jul 2009 Sep 2009 Nov 2009 Jan 2010 Date

Figure 10: Plot of the data during 2009. Note that all series are indices, created by dividing the series with their value for the ﬁrst point in the partition, which in this case is the value at 2009-01-02.

Exchange rate and Commodity indices 1.4

1.3

1.2

1.1

0.9

0.8 USDAUD Gold Crude oil 0.7 Natural Gas Iron 0.6 Jan 2011 Mar 2011 May 2011 Jul 2011 Sep 2011 Nov 2011 Jan 2012 Date

Figure 11: Plot of the data during 2011. Uncertain economic conditions and fears of a global ﬁnancial system collapse drove investors to gold, resulting in prices reaching record levels. Iron Ore saw its steepest slide ever after slowing demand from the Chinese construction sector. China consumes over half of the worlds output in iron ore. [Spechler, 2012] [Serapio, 2011]

59 Exchange rate and Commodity indices 1.3 USDAUD Gold 1.2 Crude oil Natural Gas Iron 1.1

0.9

0.8

0.7

0.6 Jan 2012 Mar 2012 May 2012 Jul 2012 Sep 2012 Nov 2012 Jan 2013 Date

Figure 12: Plots of the data during 2012. A mild 2011-12 winter, high natural gas inventories, and increased supply contributed to lower average spot natural gas prices during 2012. As production receded following lower prices, prices started to recover from June through the rest of the year. Hot weather lead to greater demand for natural gas use for power generation, contributing to the slight rise in prices during the summer months. However, prices remained lower than seen in most of 2011. After prices reaching record high levels during 2011, the price for Iron Ore fell during mid 2011. This was primarily due to a slowdown in growth in steel making in China, combined with Chinese steel mills overproducing. [USEIA, 2013] [Weisenthal, 2012]

60 Exchange rate and Commodity indices 1.4 USDAUD Gold 1.3 Crude oil Natural Gas Iron 1.2

1.1

0.9

0.8

0.7 Jan 2013 Mar 2013 May 2013 Jul 2013 Sep 2013 Nov 2013 Jan 2014 Date

Figure 13: Plots of the data during 2013. The price of gold plunged by more than 25% during 2013. Worries of a shift in the US Federal Reserves monetary policy and the Cyprus banking crisis. where investors feared a liquidation of the island nation’s gold reserve contributed to the decline. [Caplinger, 2013]

Exchange rate and Commodity indices 1.2 USDAUD Gold 1.1 Crude oil Natural Gas Iron 1

0.9

0.8

0.7

0.6

0.5 Jan 2015 Mar 2015 May 2015 Jul 2015 Sep 2015 Nov 2015 Jan 2016 Date

Figure 14: Plots of the data during 2015. Crude oil prices ended on the lowest note since 2009, reﬂecting continued excess of crude oil supply over global demand. Concerns over an increased supply as a result of lifted sanctions on Iran led to a further decrease of the price. Declining demand for iron ore in China, and cheap new supply has put pressure on the iron ore prices since late 2013. [Elliott, 2015] [Els, 2015]

61 Exchange rate and Commodity indices 2 USDAUD Gold 1.8 Crude oil Natural Gas Iron 1.6

1.4

1.2

0.8

0.6 Jan 2016 Mar 2016 May 2016 Jul 2016 Sep 2016 Nov 2016 Jan 2017 Date

Figure 15: Plots of the data during 2016. Iron ore prices recovered during 2016 as a result of steady demand from China and supply cutbacks from top producers. Natural gas spot prices reached its lowest level since 1999. Changing demand, large inventories, and temperatures warmer than usual through the year was the main factors driving the prices. Prices gradually increased during spring as demand rose and production decreased before cold winter temperatures further contributed to the hike. [Tsai & Upchurch, 2017]

Gold Crude Oil 0.4 0.6

0.4 0.2 0.2 0 0

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag Lag Natural Gas Iron 0.2 0.2

0.1 0.1

0 0

-0.1 -0.1

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag

Figure 16: Cross-correlation for 2009

62 Gold Crude Oil 0.4 0.6

0.4 0.2 0.2 0 0

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag Lag Natural Gas Iron 0.2 0.2

0.1 0.1

0 0

-0.1 -0.1

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag Lag

Figure 17: Cross-correlation for 2011

Gold Crude Oil 0.4 0.6

0.4 0.2 0.2 0 0

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag Lag Natural Gas Iron 0.2 0.2

0.1 0.1

0 0

-0.1 -0.1

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag Lag

Figure 18: Cross-correlation for 2012

63 Gold Crude Oil 0.4 0.2

0.1 0.2 0 0 -0.1

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag Lag Natural Gas Iron 0.2 0.2

0.1 0.1

0 0

-0.1 -0.1

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag Lag

Figure 19: Cross-correlation for 2013

Gold Crude Oil 0.4 0.4

0.2 0.2

0 0

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag Lag Natural Gas Iron 0.2 0.2

0.1 0.1

0 0

-0.1 -0.1

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag Lag

Figure 20: Cross-correlation for 2015

64 Gold Crude Oil 0.2 0.4

0.1 0.2 0 0 -0.1

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag Lag Natural Gas Iron 0.2 0.2

0.1 0.1

0 0

-0.1 -0.1

-0.2 -0.2 Sample Cross Correlation -20 -10 0 10 20 Sample Cross Correlation -20 -10 0 10 20 Lag Lag

Figure 21: Cross-correlation for 2016

Correlation Matrix

0.05 0.24 0.07 0.04 0 Gold -0.05

0.1 0.24 0.12 0.09

0 Crude oil -0.1 0.07 0.12 -0.01 0.1 0 -0.1 Natural gas 0.1 0.04 0.09 -0.01

0 Iron

-0.1 -0.05 0 0.05 -0.1 0 0.1 -0.1 0 0.1 -0.1 0 0.1 Gold Crude oil Natural gas Iron

Figure 22: Correlation matrix for the 2010 data.

65 Correlation Matrix 0.05 0.06 0.09 0.10

0 Gold

-0.05 0.05 0.06 0.05 -0.00

Crude oil -0.05 0.5 0.09 0.05 0.01

Natural gas -0.5 0.05 0.10 -0.00 0.01

0 Iron -0.05

-0.05 0 0.05-0.05 0 0.05 0 0.5 -0.04 Gold Crude oil Natural gas Iron

Figure 23: Correlation matrix for the 2014 data.

Normal Probability Plot 0.02 0.999

0.997

0.99 0.015 0.98

0.95

0.01 0.90

0.75 0.005

0.50 Probability 0 0.25

-0.005 0.10

0.05

0.02 -0.01 0.01

0.003

-0.015 0.001 0 50 100 150 200 250 300 -0.01 -0.005 0 0.005 0.01 0.015 Data

Figure 24: he left plot shows the estimated residuals from the regression for 2014, plotted against time. The right graph shows a Quantile-Quantile plot of the residuals.

66 9.2 Regression outputs

Coefficients Estimate SE tStat pValue ______Intercept 0.00029051 0.00063171 0.45988 0.646 Gold 0.08073 0.043813 1.8426 0.06655 Croil 0.14412 0.017097 8.4294 2.6237e-15 NG 0.004054 0.01634 0.2481 0.80425 Iron 0.040057 0.034761 1.1523 0.25026

Number of observations: 259, Error degrees of freedom: 254 Root Mean Squared Error: 0.01 R-squared: 0.263, Adjusted R-Squared 0.251 F-statistic vs. constant model: 22.6, p-value = 5.34e-16

Table 15: Model without lagged variables, y = log(returns), diﬀerenced covariates, 2009

Coefficients Estimate SE tStat pValue ______Intercept -0.00011379 0.00046257 -0.24599 0.80589 Gold 0.023474 0.028369 0.82748 0.40874 Croil 0.23677 0.023525 10.065 2.8615e-20 NG 0.032636 0.023565 1.3849 0.1673 Iron -0.073591 0.050417 -1.4597 0.14562

Number of observations: 259, Error degrees of freedom: 254 Root Mean Squared Error: 0.0074 R-squared: 0.314, Adjusted R-Squared 0.303 F-statistic vs. constant model: 29.1, p-value = 6.61e-20

Table 16: This is what perfection looks like. Model without lagged variables, y = log(returns), diﬀerenced covariates, 2011

67 Coefficients Estimate SE tStat pValue ______Intercept -1.6375e-07 0.00029881 -0.00054802 0.99956 Gold 0.12757 0.031987 3.9882 8.7005e-05 Croil 0.16804 0.022255 7.5506 7.7118e-13 NG -0.019921 0.011241 -1.7722 0.077551 Iron 0.035998 0.026915 1.3375 0.18226

Number of observations: 260, Error degrees of freedom: 255 Root Mean Squared Error: 0.00481 R-squared: 0.266, Adjusted R-Squared 0.254 F-statistic vs. constant model: 23.1, p-value = 2.63e-16

Table 17: Model without lagged variables, y = log(returns), diﬀerenced covariates, 2012

Coefficients Estimate SE tStat pValue ______Intercept -0.0004377 0.00036817 -1.1889 0.2356 Gold 0.16503 0.035365 4.6665 4.953e-06 Croil 0.035108 0.036457 0.963 0.33646 NG 0.0046384 0.017098 0.27128 0.7864 Iron -0.03649 0.031147 -1.1715 0.24247

Number of observations: 260, Error degrees of freedom: 255 Root Mean Squared Error: 0.00589 R-squared: 0.0916, Adjusted R-Squared 0.0774 F-statistic vs. constant model: 6.43, p-value = 6.07e-05

Table 18: Model without lagged variables, y = log(returns), diﬀerenced covariates, 2013

9.3 Nominal Commodity Prices Below is a list of the commodities used in this paper, accompanied by a brief description. The data has been selected according to their of the selected countries total export, and their availability:

Crude Oil, West Texas Intermediate (WTI) - Cushing, Oklahoma, retrieved from FRED, Federal Reserve Bank of St. Louis, USD/Barrel

Iron Ore, China, Average Imported Iron Ore CIF Price, USD/Metric ton

Gold, retrieved from FRED, Federal Reserve Bank of St. Louis, Gold Fixing Price 10:30 A.M. (London time) in London Bullion Market, USD/Troy Ounce

68 Coefficients Estimate SE tStat pValue ______Intercept -0.00018931 0.00047514 -0.39843 0.69065 Gold 0.17698 0.060906 2.9059 0.0039843 Croil 0.090326 0.020286 4.4527 1.2689e-05 NG 0.0080769 0.01654 0.48832 0.62575 Iron 0.026804 0.030914 0.86706 0.38672

Number of observations: 260, Error degrees of freedom: 255 Root Mean Squared Error: 0.0076 R-squared: 0.106, Adjusted R-Squared 0.0924 F-statistic vs. constant model: 7.59, p-value = 8.58e-06

Table 19: Model without lagged variables, y = log(returns), diﬀerenced covariates, 2015

Coefficients Estimate SE tStat pValue ______Intercept -0.00024728 0.00041595 -0.5945 0.55271 Gold 0.065284 0.037286 1.7509 0.081161 Croil 0.076426 0.012932 5.9097 1.0934e-08 NG 0.0040218 0.010587 0.3799 0.70434 Iron 0.022544 0.010665 2.1139 0.035497

Number of observations: 260, Error degrees of freedom: 255 Root Mean Squared Error: 0.00666 R-squared: 0.148, Adjusted R-Squared 0.134 F-statistic vs. constant model: 11, p-value = 2.82e-08

Table 20: Model without lagged variables, y = log(returns), diﬀerenced covariates, 2016

69 Country Commodity Commodity Commodity Commodity Percentage Percentage Percentage Percentage % of Export 1 2 3 4 1 2 3 4 Australia Natural gas Gold Iron Crude 7% 7% 20% 2.2% 36% Petroleum

Table 21: Selected exported commodities of Australia and percentages of export

Event Timespan Commodities Involved Speciﬁc Currencies Involved Commodities boom 2000-2014 Agriculture, oil, metals - 2000s energy crisis 2003-2008 Crude oil - Subprime mortgage crisis 2007-2009 Gold USD Greek government debt crisis 2009-2016 - Euro, European debt crisis 2009-Present - Euro Ukrainian crisis 2013-2014 - Russian ruble Russian financial crisis 2014-Present Crude oil Russian ruble Chinese stock market crash 2015-2016 Copper, cotton, soybeans Chinese Yuan

Table 22: Major Economic Events since 2000

70 Lag Gold Crude Oil Iron Natural Gas 0 1 1 1 1 1 1.336233 1.862319 1.017516 1.006394 2 1.349682 1.897501 0.985774 1.106894 3 1.513653 1.822674 0.998362 1.168726 4 1.434498 1.840121 1.037434 1.081909 5 1.381118 1.876799 1.023219 1.118870 6 1.496405 1.880863 1.059929 1.069387 7 1.398668 1.947943 1.030811 1.131537 8 1.445743 1.916924 1.053669 1.173045 9 1.376593 1.744705 1.122516 1.111593 10 1.254427 1.880878 1.004695 1.140452 11 1.409021 1.853632 1.035053 1.213957 12 1.519216 1.911945 1.060118 1.236449 13 1.222323 1.884001 1.070541 1.190256 14 1.414937 2.055312 1.045311 1.211478 15 1.529393 2.254870 1.042609 1.275947 16 1.450546 2.113394 1.084921 1.259064 17 1.396264 1.911420 1.053835 1.166809 18 1.366889 2.023599 1.026762 1.177074 19 1.429018 2.016858 1.067844 1.367082 20 1.310624 1.901829 1.100381 1.346923 21 1.437761 2.006129 1.086618 1.282400 22 1.294872 1.995560 1.081442 1.266484 23 1.331450 2.090709 1.060193 1.237159 24 1.312935 2.041580 1.107525 1.166574 25 1.346667 1.977514 0.989382 1.293863 26 1.236348 2.202997 1.068153 1.095349 27 1.414031 2.014251 1.051031 1.092891 28 1.479394 2.010969 1.052949 1.104248 29 1.453619 1.967595 1.072991 1.187351 30 1.238939 1.772300 1.052100 1.146121

Table 23: Values for the similarity measure at diﬀerent lags, given in the ﬁrst column, for 2010. The values in each column are index using the respective value at lag 0 and show the relative increase or decrease in similarity for each lag and covariate.

TRITA -MAT-K 2017:04 ISRN -KTH/MAT/K--17/04--SE