Oil price spillovers : analysing the effect of oil price changes on four major grains using an ARDL-Model

(1)

Oil price spillovers:

Analysing the effect of oil price changes on four

major grains using an ARDL-Model

University of Amsterdam Faculty of Economics and Business

Master Thesis Economics

Track: International Economics and Globalisation Bart Hoffmann

5870747

bart.hoffmann@student.uva.nl Supervisor: Drs. Naomi Leefmans Second reader: Dr. Kostas Mavromatis November 2015

(2)

2

Abstract

In this thesis the effect of changes in the oil price on four major grains (soybeans, wheat, maize and rice) is investigated using monthly price observations for a period of over 35 years. An autoregressive distributed lag (ARDL) model is used to empirically investigate this relationship. Literature has shown that there are various ways in which the oil price has an effect on food commodity prices. This can be both direct by changing production costs for food crops or indirectly via the derived demand for biofuels or changes in the US dollar exchange rate. The empirical findings show that the oil price only plays a significant role for those crops that can be produced both for consumption purposes as well as for inputs in the production of biofuels, namely soybeans and maize. This thus provides support for the hypothesis that the oil price impacts food commodity prices only indirectly via the derived demand for biofuels.

Statement of Originality

This document is written by Student Bart Hoffmann who declares to take full responsibility for the contents of this document.

I declare that the text and the work presented in this document is original and that no sources other than those mentioned in the text and its references have been used in creating it.

The Faculty of Economics and Business is responsible solely for the supervision of completion of the work, not for the contents.

(3)

3

1. Introduction

During the years of 2007-2008 global food prices saw very significant price increases. Drawing upon data from the IMF Cross Country Macroeconomics Statistics it can be seen that in the 30 months from January 2006 until July 2008 the price of maize increased by 160 percent. The market for soybeans experienced a similar price increase during this period and the price of rice increased by 181 percent. Wheat saw a relatively smaller increase in its price of 96 percent during these 2,5 years. Not only has the level of food prices seen large increases since 2007, the increase in volatility of these prices has also been significant, which is clear from figure 1 below.

Figure 1: Food and Crude Oil Prices, 1980- July 2015.

Graph constructed by the author using data from the IMF Cross Country Macroeconomics Statistics.

Together with the peak in food prices, research into the determinants of the price of food

commodities also saw an increase. In the literature several determinants of food prices have been put forward and have also been empirically tested. These determinants can be broadly classified into two groups. The first group are the factors that influence the price via the demand-side. These are for example the development of economic activity and population growth. In this case, specific attention is pointed towards fast growing economies with large populations such as India and China, which are argued to have significantly fueled demand and thus prices of food commodities. Another possible factor that affects demand and thus food prices is speculation on the food market. The second group of determinants of food prices are the supply-side determinants. Important factors

0 20 40 60 80 100 120 140 160 0 200 400 600 800 1000 1200 1-1 -19 80 1-7-1981 1-1-1983 1-7-1984 1-1-1986 1-7-1987 1-1-1989 1-7-1990 1-1-1992 1-7-1993 1-1-1995 1-7-1996 1-1-1998 1-7-1999 1-1-2001 1-7-2002 1-1-2004 1-7-2005 1-1-2007 1-7 -20 08 1-1-2010 1-7-2011 1-1-2013 1-7-2014 Wheat Maize Soybeans Rice Crude Oil

(5)

5

within this group include weather conditions that affect agricultural productivity and specific trade policies such as export restrictions. Furthermore, the increased popularity of the production of biofuels has increased demand for crops such as maize and soybeans for this purpose. This is turn has had an effect on supply of these crops for consumption purposes.

A further important factor that is mentioned in many papers investigating determinants of food prices is the oil price, which is usually seen to affect food prices through the supply-side as increases in the oil price increase production costs of food commodities. Figure 1 above indeed shows that there seems to be a strong link between the price of crude oil and the prices of several food

commodities. Several papers investigating the main drivers of food prices have found the oil price to be one of the most important determinants of food prices (e.g. Abbott et al.(2009) and Headey and Fan(2008)). However, relatively few research has been done that focuses solely on the complex relationship between oil and food prices.

There are several ways in which food prices could be affected by the oil price. One could argue that an increase in the oil price increases the production costs of agricultural goods, since this production process relies heavily (especially in the US) on machines that need petrol. Increasing the production costs will increase the price of the agricultural output and thus oil prices and food prices are

positively linked, which is shown by Abbott et al.(2009) to be the result of many previous papers. Furthermore, papers such as that of Chen et al.(2010) have argued that an increase in oil prices will increase the demand for biofuels, since this is seen as a substitute product for petrol. Considering the fact that biofuels are made using agricultural output such as maize and soybeans, this substitution effect will increase demand for these crops and thus increase their price. This is therefore another, although indirect way in which oil price changes affect the price of food commodities. Other papers have also argued that there are further indirect linkages that play a role in the oil-food relationship. Oil price increases could have an effect on the US dollar exchange rates and via that way have a further impact on food commodity markets.

It thus seems that changes in the oil price could affect food commodity prices through different channels. This thesis aims to investigate the relationship between the oil and food market more closely and provide insight into these different channels through which oil price changes result in changes on the food market. The focus in this paper will be on a selection of four food commodities, namely soybeans, wheat, maize and rice. The research question it tries to answer is therefore: to what extent do changes in the oil price affect prices of food commodities?

To answer this research question this thesis will first focus on previous literature concerning this topic. A very short introduction of several determinants that play a role in determining food prices

(6)

6

will be given. The literature review then continues with a more in-depth look at previous work on the relationship between food and oil prices. After that an empirical framework is constructed , whereby the prices of four food commodities (soybeans, wheat, maize and rice) will be used as dependent variables and these will be regressed on the crude oil price and several other factors. The model will be based on the paper by Chen et al.(2010) who use an autoregressive distributed lag (ARDL) model. As argued later, this model is able to capture both the short-run and long-run dynamics of this relationship.

I will enhance their model in two ways: firstly, they only focus on three food commodities, whereas this paper will also focus on one additional food commodity, namely rice. Since the markets for agricultural products is heavily integrated, I expect that shocks in one market have an effect in other markets. Therefore I will also include rice in my analysis, since this is one of the most important food crops in production and trade on the world market. Additionally I will include a variable to account for the US dollar exchange rate, since previous literature has argued that this is an important factor in the oil-food price relationship. Monthly data for the four food commodities under investigation will be gathered from the IMF’s Cross Country Macroeconomics Statistics. The price of crude oil will also be gathered from this database. Data for the US dollar exchange rate will be collected from the United States Federal Reserve system.

The remainder of this thesis will be structured as follows: Chapter 2 will provide a very brief overview of the main determinants of food prices as discussed in previous literature. Chapter 3 will then zoom in on the relationship between oil prices and food prices and distinguish three separate ways in which the oil price affects food commodity prices: a direct cost-push effect, the derived demand for biofuels and an indirect effect through the US dollar exchange rate. Chapter 4 will specify the empirical framework that will be adopted and will continue by testing several aspects of the proposed model and variables. Subsequently, chapter 5 will provide the estimation results and discussion of these results. The final section will provide concluding remarks.

(7)

7

2. Main determinants of food commodity prices

Especially since the price boom in the global food market, a large number of papers have been published that investigate the determinants of food prices. Determinants of food prices are usually separated in two distinct groups: factors that determine food prices via the demand side and supply-side determinants. This section provides a short overview of the main proposed determinants of food prices that have been put forward by previous literature. As this thesis focuses on the oil price as a determinant of food prices, the following discussion of other determinants will be relatively brief and therefore this section does not claim completeness.

2.1 Demand-side determinants

Population and GDP growth

A first determinant of rising food prices that is often been put forward is a rather intuitive one, namely the increase of demand through both increases in the growth of economies worldwide as well as an increase in the worldwide population. Especially populous countries that have seen large economic growth over the last decade such as India and China are believed to be at the center of this. Intuitively, it seems logical that large increases in population have attributed to the increase in demand and thus in prices of food commodities. Another argument to support this rationale is the idea that not only direct consumption of food crops have increased in these countries, but that increases in per capita income have shifted the average diet. Demand has also been pushed upwards by a shift towards higher meat consumption per capita and thus higher demand for food

commodities as feed grain for cattle (FAO, 2008). As India and China together make up almost 27% of world population, even a small shift in food demand or dietary patterns in these countries would indeed be likely to have significant effects on global food markets.

Headey and Fan (2008) reject the proposition that increased demand from India and China has played an important role in the recent food price surges. They show that both China and India are mostly self-sufficient when it comes to the most important grains. China imported less wheat during the period of 2000-2008 than the preceding 8 years and rice imports also declined moderately. A similar pattern is true for India, where imports of maize and wheat are negligible and it is actually a net exporter of rice. It is interesting to note that Headey and Fan (2008) do see a theoretical way in which increased population and GDP growth could contribute to higher commodity prices, namely in an indirect way by increasing demand for oil in these countries.

Similar statistics are found by the Food and Agricultural Organization, with their 2008 report showing that grain imports of China have actually decreased by 4% on average since 2001 (FAO, 2008). Baffes and Haniotis (2010) agree with this conclusion, after investigating growth trends of both population

(8)

8

and income together with demand for food commodities over the last few decades. They conclude that there is no evidence of accelerating food demand in India, China or the world as a whole leading to the peaks in food commodity prices. As a matter of fact, their data shows a decrease in the

demand growth for most grains. Only for maize one could see that demand growth indeed increased, a finding they explain by the rising demand for biofuels produced with maize (e.g. ethanol), rather than an increase in demand for maize for food consumption purposes.

Biofuels

The previous section briefly touched upon the issue of biofuels as a possible explaining factor of food price increases. This determinant has been gaining attention over the last decade, since both

demand and production of biofuels have rapidly increased. This thesis will focus on the two main biofuels: ethanol which is mainly produced using maize and biodiesel that is produced with soybeans as the main input.

The main idea is that an increase in the demand for biofuels will put upward pressure on the price of food commodities, namely maize and soybeans in this case. More of the harvests will be put to use in producing biofuels, diminishing supply on the markets for these crops when it comes to consumption purposes and thus increasing their price. The two figures below are taken from Cooke and Robles (2009) and indeed show a sharp upward trend in US production of biofuels during the 2006-2008 price hikes on the global food market.

(9)

9

Figure 3: US biodiesel production

Via the mechanism explained above, one could suppose that the increased production of biofuels has indeed attributed to the price increases of food commodities, and many papers have indeed found this to be true. We must however also take into account the underlying reason that demand and production of biofuels have taken off since 2000. Biofuels are seen as a substitute for petroleum and thus a rising oil price makes it more attractive to switch to biofuels. Indeed, Schmidthuber (2008) has shown that once the oil price increases above 58 US dollar a barrel, it becomes profitable to produce biofuels. An increase in the oil price will thus not only directly affect crop prices, but will also increase demand for and production of biofuels, thereby decreasing supply on the market for food

consumption. Since biofuels and the price of oil are linked this way, a further description of the effect of biofuels on food commodity prices will be postponed to chapter 3.

Speculation

Another determinant put forward as fueling food commodity prices is the increased activity of financial speculation in these markets. It is indeed the case that the US Commodity Futures Trading Commission (CFTC) has loosened the rules concerning who is able to trade in agricultural market, thereby opening up the market to players such as index funds and other nontraditional participants. These speculators are entering in either long or short positions in agricultural contracts, with the hopes of either buying or selling commodities in the future with a profit. As large index funds mainly take a long position in commodity markets, this reflects the fact that the general expectation is that food prices will rise in the future. This expectation of future price increases will in turn induce pressure on current prices to increase (De Schutter, 2010). The theoretical reasoning seems straightforward and many authors have shown that speculative activities have indeed increased in food markets (see Cooke and Robles (2009), Baffes and Haniotis (2010) and Irwin et al.(2007)).

(10)

10

Previous literature is however not conclusive about whether or not speculation can be seen as an important determinant of food prices with both strong opponents as well as supporters of this hypothesis. A policy brief by the Conference Board of Canada (CBC, 2008) for example argues that there is no clear causal linkage between the two. Rather than speculation being a cause of increases in both the level and volatility on food markets, they see speculation is a symptom of this increased volatility. Headey and Fan (2008) also support this view, concluding that increased activity on future commodity markets may have exacerbated the volatility in these markets, but that there is little evidence that this has influenced real demand and supply. In their 2009 paper, Cooke and Robles however find the exact opposite: out of several possible explanations tested, financial activity in future markets and other proxies for speculation turn out to be the only determinants that are shown to explain observed changes in prices. Gilbert (2009) also finds some evidence that prices in certain commodities increased due to increased speculative activity. He finds the existence of so-called commodity bubbles in several markets, most importantly in the market for soybeans.

2.2 Supply-side determinants

Weather shocks

It is clear that adverse weather shocks could play a role in determining the harvest of a particular food crop. Severe floods or droughts in a country that is a major producer of a crop will cause a drop in world supply and thus increase the world price. Food production has also seen large increases in its scale, concentrating the production of certain crops in relatively few exporting countries. This could increase the importance of weather shocks in determining supply. Headey and Fan (2008) provide examples of supply shocks for the global wheat market. Global wheat production dropped by 5% in 2006/2007, particularly due to a poor harvest in Australia which was 60% below its trend growth rate due to extreme droughts. Simultaneously, the US also experienced a poor harvest with declines of 14%. Although it is attractive to view this as the main cause of prices surges, it is shown that this is not the case. Production shortfalls of wheat are not uncommon: global wheat production declined by 11% in 2000/2001 and 6% in 1993/1994, without large increases in global wheat prices as has been the case in 2006/2007. They thus argue that variability in weather and production is normal in commodity markets and cannot be seen as the main driver of the recent price increases, but merely as a minimal determinant of food prices. Also, adverse shocks to production due to extreme weather could at least partly be countered by depleting food reserves.

Trade restrictions

Next to weather shocks, changes in domestic policies concerning exports of food crops could also have an effect on food prices. Headey and Fan (2008) argue that this argument could hold for

(11)

11

specific crops but not for food markets in general. The only food commodity for which they believe this could be a determining factor is rice. This is due to the fact that rice is relatively thinly traded compared to other commodities, meaning that only a small portion of world production is

internationally traded. A decrease in trade volume due to an export restriction will then have a larger impact on global supply and thus prices. Figure 4 below suggests that the reactions of traders to export bans in major rice producing countries could possibly be a factor attributing to the sharp rise in prices. Also, a number of rice importing countries, most notably the Philippines, displayed clear hoarding behavior, adding to the already upward pressure on rice prices.

Figure 4. Export restrictions and rice prices

Source: Headey and Fan (2008).

The oil price

Figure 1 in the introduction already showed a strong relationship between the oil price and food prices and that these have moved together during the price hikes of 2006-2008. As oil is an important input factor in the production, a positive relationship is to be expected between the oil price and food prices. Mitchell (2008) shows that for every acre of wheat produced in 2007 in the US, the fuel costs are 19.20 dollar. Maize is even more fuel-intensive to produce, with fuel costs of 30.98 dollar per acre. Other inputs used in food production also rely on fuel, such as the production of fertilizers. It is thus easy to reason that an increase in the price of oil will increase production costs and thus also the prices of food commodities. Apart from these direct effects however, there are also other channels through which the oil price and food prices are linked. The next chapter investigates these channels in more detail.

(12)

12

3. The relationship between the oil price and food commodity prices

Although the oil price is seen as an important factor in many of the papers discussed in chapter 2, relatively few research has been done that focuses solely on the complex relationship between oil and food prices. This chapter provides an overview of several papers that have focused on this relationship to describe several channels through which the price of oil can influence the price of food commodities. The first section starts with describing the most straightforward linkage through which this happens: the cost-push effect. Thereafter two other linkages will be discussed, namely the demand for biofuels and the impact of the US dollar exchange rate.

3.1 Cost-push effects

Many authors have looked at the relationship from a point of a cost-push effect as this is the most logical way of thinking about the link between oil and food prices. Abbott et al (2009) provide a literature review of 25 studies of the world food crisis of 2007-2008 to identify the main drivers of food prices. The linkages between oil prices and food markets was found to be one of the three most important determinants of food prices. They find that especially since 2006 the energy and

agricultural markets became closely linked. Headey and Fan (2008) also provide evidence that oil price increases directly increase food prices due to the cost-push effect, since agricultural production is still heavily reliant on oil input. Furthermore, oil is an important input for the production of

fertilizers and since fertilizers in some cases account for up to 20% of operating costs in food production, this further strengthens their claim. In their estimation analysis, they compare the price of corn, wheat and soybeans including all oil-price related inputs of agricultural production to a baseline scenario where oil prices would have only increased by average US inflation over the period 2001-2007. They find that oil prices increased the cost of production between 30-40% over this period, depending on the particular food commodity. They however do not investigate causality.

Baffes (2007) provides a very extensive, although basic, research into the pass-through effects of crude oil prices, also focusing on the cost-push effect. He does however also incorporate inflation as a controlling variable. In his model he looks at the effect of changes in this price on the price of 35 commodities over a period of 45 years. His research shows that the largest pass-through effect was seen in fertilizers, with a figure of 0.33, meaning that a 10% increase in oil prices has led to a 3.3% increase in the price of fertilizers. Oil price surges thus increase the input costs of agricultural production. Similarly, figures of around 0.18 were found for the pass-through of oil prices on

agricultural commodities, thereby strengthening the belief that oil and food prices are positively correlated.

(13)

13

3.2 Derived demand for biofuels

Although the previous mentioned papers provide a solid foundation, much of the literature has argued that solely focusing on the cost-push effect is too simplistic and that other factors need to be taken into account. The most important other factor is the production of and demand for biofuels. As briefly discussed in chapter 2, this thesis focuses on ethanol and biodiesel. The former is produced using maize as inputs and biodiesel uses soybeans as an input factor. One of the papers to look at this relationship is that by Chen et al.(2010). They construct an empirical framework to investigate the relationship between the crude oil price and the global prices for corn, soybean and wheat. In their analysis they incorporate the market of biofuels, by also including the price of other crops as explanatory variables. In this they fall back on the paper by McConnell (1989) that provided a

theoretical framework for cropland allocation, which will be discussed below. Chen et al.(2010) argue that demand for biofuels has been rising which increases the price of the land used to cultivate these crops, resulting in higher food prices. This process is enhanced by the rise of oil prices that causes demand for the substitutive biofuels to increase, thereby increasing demand for crops. In other words, different crops are in competition with each other for planted areas. High soybean and maize prices, for example due to high biofuel demands, will give an incentive to increase area planted with these crops. This in turn reduces areas planted with other crops such as wheat, which will increase the price of wheat. They use an autoregressive distributed lag (ARDL) model with data of weekly prices over the period 1983 to 2010. Their analysis shows that the change in each of the above mentioned commodities is significantly influenced by the changes in the crude oil price, especially in times of already high oil prices. This result is most obvious for the price of soybeans, where in a certain subperiod of the time investigated, a 1% increase in the price of oil increases the price of soybeans by 155.50%. Prices of both wheat and maize are also shown to be influenced by oil prices, although this relationship is less striking. They however do not perform any causality tests.

The theoretical framework Chen et al. (2010) use is based upon the modelling by McConnell (1989) as mentioned above. McConnell has developed a cropland allocation model that explains the influence of different crop prices on each other, which Chen et al. (2010) extend to a theoretical framework they call the Global Cropland Allocation model.

The starting point of this model is the assumption that cropland endowment is fixed at A and cropland can be either used to produce food crops for consumption 𝐴𝐹 or to produce food crops for

energy production 𝐴𝐸. In this thesis, we look at the four major crops, where soybeans and maize can

be either used for food or energy production and wheat and rice are solely produced for food purposes. The amount of land dedicated to the production of a certain crop is denoted by X, where 𝑋𝑊 and 𝑋𝑅 denote acreage for wheat and rice respectively. Similarly, 𝑋𝑆𝐹 and 𝑋𝑀𝐹 denote acreage for

(14)

14

soybeans and maize for food purposes, whereas 𝑋𝑆𝐸 and 𝑋𝑀𝐸 denote acreage for these crops for

energy purposes. To generalize this model i is taken as a particular food commodity, while j is a certain biofuel. Fundamentals of the model will then be as following:

Inverse demand function of ith food crop: 𝑃_𝑖𝑑 (𝑄_𝑖𝑑) Inverse demand function of jth biofuel: 𝑃𝑗𝑑 (𝑄𝑗𝑑)

Production cost per hectare for ith food crop 𝑇𝐶𝑖𝐹

Production cost per hectare for ith energy crop 𝑇𝐶_𝑖𝐸 Production cost for jth biofuel 𝐶𝑗 (𝑄𝑖𝑑)

Crop yield for ith food crop 𝑌𝑖

Transformation rate from ith food crop to jth biofuel 𝐵𝑌𝑖𝑗

Using the above equation the model continues by setting up the objective function, further referred to as the global social welfare, and several constraints.

Max: ∑𝑛_𝑖=1[∫ 𝑃_𝑖𝑑 (𝑄_𝑖𝑑)𝑑𝑄_𝑖𝑑- 𝑇𝐶𝑖𝐹𝑋𝑖𝐹] + ∑𝑚𝑗=1[∫ 𝑃𝑗𝑑(𝑄𝑗𝑑)𝑑𝑄𝑗𝑑- 𝐶𝐹𝑋𝑖𝐹] - ∑𝑛𝑖=1𝑇𝐶𝑖𝐸𝑋𝑖𝐸 (1)

Subject to:

∑𝑛𝑖=1(𝑋𝑖𝐹+ 𝑋𝑖𝐸) ≤ 𝐴 (2)

-𝑌𝑖𝑋𝑖𝐹+ 𝑄𝑖𝑑≤ 0 (3)

- ∑𝑛𝑖=1𝐵𝑌𝑖𝑗𝑋𝑖𝐸+ 𝑄𝑗𝑑 ≤ 0 (4)

Equation (2) gives the global land restraint, equation (3) gives the demand and supply balance constraint for food crops, while equation (4) gives the demand and supply balance constraint for biofuel crops. Equation (1) is the global social welfare function. The first part is the area under the food crop demand curve minus total cost, the second part is analogous but then for biofuel crops, while the third part gives the total cost of producing energy crops.

The following step is setting up the Lagrangian, where γ, µ𝑖 and λ𝑗 are the shadow prices that follow

from equation (2) – (4). After that, the four first-order conditions are presented.

L= ∑𝑛_𝑖=1[∫ 𝑃_𝑖𝑑 (𝑄_𝑖𝑑)𝑑𝑄_𝑖𝑑- 𝑇𝐶𝑖𝐹𝑋𝑖𝐹] + ∑𝑚𝑗=1[∫ 𝑃𝑗𝑑(𝑄𝑗𝑑)𝑑𝑄𝑗𝑑- 𝐶𝐹𝑋𝑖𝐹] - ∑𝑛𝑖=1𝑇𝐶𝑖𝐸𝑋𝑖𝐸 + γA

(15)

15 𝜕𝐿 𝜕𝑄_𝑖𝑑= 𝑃𝑖 𝑑_{− µ} 𝑖 = 0 𝜕𝐿 𝜕𝑄_𝑗𝑑= 𝑃𝑗 𝑑_{− MC} 𝑗− λ𝑗 = 0 𝜕𝐿 𝜕𝑋_𝑖𝐹= −𝑇𝐶𝑖 𝐹_{+ µ} 𝑖𝑌𝑖− γ = 0 𝜕𝐿 𝜕𝑋_𝑖𝐸= −𝑇𝐶𝑖 𝐸_{+ λ} 𝑗𝐵𝑌𝑖𝑗− γ = 0

Rearranging gives the following two equilibrium conditions:

𝑃_𝑖𝑑𝑌𝑖 = 𝑇𝐶𝑖𝐹+ γ (5)

𝑃_𝑗𝑑𝐵𝑌𝑖𝑗= 𝑇𝐶𝑖𝐸+ MC𝑗𝐵𝑌𝑖𝑗+ γ (6)

The left-hand side of equation (5) equals the marginal revenue of producing the ith food crop, which equals the right-hand side marginal costs of production. These costs include production costs (𝑇𝐶𝑖𝐹)

and land rent cost per hectare (γ). A similar interpretation holds for marginal revenue and costs for production of biofuels according to equation (6). These two equilibrium conditions show the linkage between grain prices and energy prices. The quantity of food crops and biofuels demanded depend on the prices of biofuel, prices of food crops, the production technology and production costs. An empirical confirmation of this theoretical framework is provided by Timilsina et al.(2010). In the setting of a global dynamic computable general equilibrium model they investigate long-term impacts of demand for biofuels on food availability, food prices and income amongst others. They indeed find evidence of a switch towards acreage of land used to produce energy crops such as sugar crops, maize and other lower quality crops used as inputs for ethanol. Furthermore, global food supply is shown to be expected to decrease moderately. This effect is more prominent in middle- and low-income countries. Finally, several groups of food commodity prices are shown to be increasing due to expanding biofuel demand, with a maximum of 9.2 to 11% for sugar crops.

Other papers also look at the role of biofuels through formalized econometric modelling, such as Rosegrant et al.(2008). Focusing on long-term relationships and employing a Generalized Equilibrium Model they find large positive relationships between food prices and demand for biofuel over the period 2000-2007. The price impact for rice and wheat are shown to be 21% and 22% respectively. Impact on maize prices is the largest, which they show to be 39% over this eight-year period.

(16)

16

Headey and Fan(2008) also examine the relationship between the market for biofuels and food prices. They claim that the 75% rise in soybean prices from April 2007 to April 2008 can be largely explained this way. Over this period, land used for maize production was rapidly expanded by 23% to meet increased demand for biofuels, causing a 16% decline in soybean area which put an upward pressure on global soybean prices. They provide an overview of various research papers which have also used estimation models to quantify this relationship, arguing that up to 60% of price increases can be accounted for by biofuels. Although Headey and Fan(2008) see room for improvement in these models, they agree that there are significant positive relationship between the demand for biofuels and food prices, especially on the global market for corn. One of their most important suggestions for improvement is including exchange rate effects of the US dollar in the econometric framework, which will be looked at in the next section.

3.3 US dollar exchange rate effects

Another transmission mechanism through which changes in the oil price can affect agricultural commodity prices is through the relative strength of the US dollar. Nazlioglu and Soytas (2012) argue that this indirect effect cannot be ignored when examining the relationship between oil and food prices. The US dollar denominates most commodity trade worldwide and as such the strength of the dollar should be taken into account. In their paper they try to determine to what extent world oil prices and the relative strength of the US dollar influence the prices of 24 world agricultural commodity prices. Since a change in oil prices has a significant effect on the current account of the US this will affect the exchange rate. This relationship is also explained by Abbott et al. (2009). They show that agricultural commodity prices as well as oil prices denominated in dollars have closely followed the path of exchange rates. They argue that as the crude oil price increases, total costs of US imports increase, thus worsening the trade balance which will put a depreciating pressure on the dollar. They thus argue that this exchange rate effect needs to be taken into account to look at the total effect of oil prices on food prices. Furthermore, their descriptive analysis shows that there exists a negative relationship between the US dollar exchange rate and commodity prices. By constructing several tables and graphs they compare changes in commodity prices denominated in different currencies. Figure 5 below is taken from Abbott et al.(2009), showing the evolution of prices of the four main food crops denoted in terms of nominal US dollars, real Euros and by dollars adjusted by the US Department of Agriculture (USDA) exchange rate index. This figure clearly shows that the 2006-2008 age of food price inflation was much more pronounced in dollar terms than in other currencies.

(17)

17

Figure 5: Agricultural commodity prices in various currencies, 1990-2009

It therefore seems justified to incorporate the strength of the US dollar in any analysis when

investigating linkages between the crude oil price and commodity prices that are denominated in US dollar. As mentioned above, Nazlioglu and Soytas (2012) investigate this relationship for a total of 24 different world agricultural commodity prices, including the four commodities that this thesis will focus on. To perform this research they utilize a panel cointegration analysis, enabling them to capture the relationship between the three series. Hereby they were the first to use such a

framework in the literature concerning this relationship. They show that the oil price has a significant effect on the prices of the different commodities, with the analysis of 21 out of 24 commodities showing a positive and statistically significant coefficient for the oil price variable. Although statistically significant, the magnitude of this coefficient is between 0.2 and 0.4 for most of the commodities investigated and therefore considered relatively small. They find statistically significant relationships for all four commodities investigated in this thesis, ranging from a coefficient of 0.23 for soybeans to 0.32 for wheat and rice. They also perform Granger causality tests and show that both oil prices and the exchange rate of the US dollar are Granger causes of agricultural commodity prices. It is interesting to note that the same authors found different results when looking at the Turkish market. In their 2010 paper, Nazlioglu and Soytas use a generalized impulse-response analysis and the Toda-Yamamoto causality approach to investigate the relationship between world oil prices, agricultural commodity prices in Turkey and the lira-dollar exchange rate. Neither the exchange rate or the oil price Granger causes the prices of three out of five (wheat, cotton and soybeans)

(18)

18

commodities they investigate, while for maize and sunflower oil only the exchange rate Granger causes these prices. They do not find any statistically significant long-run relationship and thus conclude that oil prices affect commodity prices in Turkey neither directly or indirectly through the exchange rates (Nazlioglu and Soytas, 2011)

Both Gohin and Chantret (2009) and Cooke and Robles (2009) however are examples where the strength of the US dollar is taken into account but a statistically significant and negative

relationship between the crude oil price and the price of food commodities is found. Using a Computable General Equilibrium (CGE) model Gohin and Chantret (2009) investigate the long-run relationships between these two prices. The crucial addition of their paper to the existing literature is that they also include several macro-economic linkages which have not been investigated thus far, including the effect of changes in the US dollar exchange rate. Since they also investigate a similar model while excluding these macro-economic identities, much can be said about their importance. When disregarding the macro-economic linkages they find similar results, namely that an increasing oil price also increases the price of food commodities through a cost-push effect. Surprisingly, they find opposite results concerning the effects of oil prices on food prices when these macro-economic linkages are included. Taking account of these they show that, especially for oil importing countries like the US and EU-countries, price rises in the oil market could reduce real income. Depreciation of the currency will worsen the trade balance, and a price rise of oil will reduce disposable income. This in turn decreases expenditure on and demand for food commodities, resulting in a negative

relationship between the two prices. They thus argue that these macro-economic linkages overrule the cost-push effects.

Cooke and Robles (2009) also investigate the oil-food relationship while adding biofuels and the USD/Euro exchange rate. They model the price of four commodities (maize, wheat, rice and soybeans) using a first-difference time series analysis. In its core this shows similarities to the model of Chen et al.(2010), but as mentioned Cooke and Robles also add the exchange rate and several other exogenous explanatory variables. The oil price is shown to either have a weak or no

explanatory power for the changes in food commodities. Only for the price of soybeans and maize do they find that oil price is a weak explanatory factor, and similar to Gohin and Chantret this

relationship is shown to be negative. As the vast majority of the literature has found a positive relationship, this is a surprising result. One possible explanation they put forward is the fact that ethanol can only be combined with gasoline in a proportion not exceeding 10 percent. If there is a fixed relationship between gasoline and ethanol in consumption, rather than substitutes, ethanol and gasoline can now be seen as complimentary goods. Higher oil prices will then cause a drop in demand for ethanol and consequently result in a lower price of maize. However, they also note that

(19)

19

there is no further evidence of this mechanism, as they do not find a statistically significant relationship between ethanol production and maize prices.

Overall, the large majority of the literature finds the oil price to be a significant determinant of food prices. Furthermore, this relationship is usually found to be positive, where an increase in the price of oil both directly and indirectly pushes the prices of food commodity upwards. This thesis now

continues by setting up an empirical framework to test the relationship between the oil price and the price of the four major grains.

(20)

20

4. Empirical Model

This section will provide the empirical model used to run the regression to assess whether there is a statistically significant relationship between the price of a certain food commodity and the price of oil, the price of other food commodities and the US dollar exchange rate. The model will be based on the framework used by Chen et al.(2010). In their model, they regress the price of one of three food commodities (soybeans, wheat and maize) on lagged values of that same commodity, both the current oil price and lagged value of the oil price and lagged values of the other two food commodities. They thus employ an Autoregressive Distributed Lag (ARDL) model.

In the next section, the methodology and variables used will be discussed. Starting in section 4.2, several paragraphs investigate the correct empirical framework to be used. Firstly, the least squares assumptions will be discussed, followed by a paragraph to determine the appropriate number of lags. Sections 4.4 and 4.5 will test for multicollinearity and nonstationarity respectively. These tests are followed by section 4.6 which will look at the possible presence of heteroscedasticity. Concluding, section 4.7 will specify the correct model to be employed.

4.1 Data and Methodology

For this thesis, a time period of 35 years will be used, as the monthly data for food commodities is available from January 1980 onwards. These monthly prices for the four food commodities included are taken from the IMF’s Cross Country Macroeconomic Statistics. The price of crude oil is also taken from these statistics. The value of the exchange rate of the US Dollar is taken from the United States Federal Reserve System (FED). What follows is a more detailed description of the variables included1

SOY is the monthly price of so-called No.2 yellow soybeans in US dollars per metric ton. These prices are forward contracts as quoted on the Chicago Board of Trade (CBOT).

WHEAT is the monthly price of type No.1 Hard Red Winter, ordinary protein. Again these prices are quoted in US dollar per metric ton.

MAIZE is the monthly price of US No.2 Yellow type maize in US dollar per metric ton.

RICE is the monthly price of 5 percent broken milled white rice according to Thailand nominal price quotes, converted into US dollar per metric ton.

1_{Both the IMF and the FAO use these specific types of the grain in determining prices, and thus these can be}

(21)

21

OIL is the monthly price of Dated Brent, light blend 38 API oil, measured in US dollar per barrel.

USX is the monthly index of the exchange rate of the US dollar as quoted by the FED, where March 1973 is used as the base month (March 1973=100). It is the so-called FED Major Currency Index, meaning it is a weighted average of the foreign exchange values of the US dollar against a subset of currencies as determined by the FED.

Monthly data for all these variables of the complete time period under consideration is available. Every variable thus has 427 observations

This thesis will employ a so-called Autoregressive Distributed Lag (ARDL) model to investigate the relationship between food and oil prices. As briefly touched upon in chapter 3, when modelling short-term dynamics in models estimating energy demand relationships in the context of time-series, this is the most appropriate and widely used econometric framework(Chen et al.(2010), Benten and Engsted(2001)). In this model, the term ‘autoregressive’ refers to the fact that past values of the dependent variable may be able to explain its current value, and therefore lagged values of this dependent variable. Furthermore, apart from including current values of explanatory variables which deal with instantaneous effects on the dependent variable, lagged values of the independent

variables are also included. The effects of independent variables on the current value of the dependent variable are thus being studied over several time periods, thus justifying the word

‘distributed’ in the name of the model. Overall this gives rise to a model that can explain the dynamic relationship between several independent variables and the dependent variable, accounting for both short-run and long-run relationships through the included lags of the variables under investigation.

The format of the empirical framework will thus be an ARDL model, where the price of a certain food commodity will be regressed on lagged values of itself and the oil price. Chapter 3 has also shown that the US dollar exchange rate could be an influencing factor in determining price of crops. Furthermore, the extension of the McConnell cropland allocation model (McConnell, 1989) as described before gives theoretical justification for the inclusion of lagged values of other crop prices in determining the price of a food commodity. Including lagged values both of the dependent variable itself and the independent variables will give the proposed ARDL model below:

𝑆𝑂𝑌

_𝑡

= 𝛼

₀

+ ∑

𝑇_𝑙=1

𝛼

₁

𝑆𝑂𝑌

_𝑡−𝑙

+ 𝛽

₀

𝑂𝐼𝐿

_𝑡

+ ∑

𝑇_𝑙=1

𝛽

₁

𝑂𝐼𝐿

_𝑡−𝑙

+ 𝛾

₀

𝑊𝐻𝐸𝐴𝑇

_𝑡

0

𝑅𝐼𝐶𝐸

𝑡−𝑙

(22)

22

In this case, the price of soybeans is chosen as the dependent variable, but the model is analogous in case any of the other crops are used as the dependent variable.

4.2 Least squares assumptions of the ARDL model

Following from Stock and Watson (2012), there are four main assumptions that need to hold to be able to conclude that the OLS regression in the context of an ARDL model will yield appropriate estimators of the unknown coefficients. The estimators will then have sampling distributions that are unbiased, consistent and asymptotically normal.

The first of these so-called least squares assumptions is that 𝑢𝑡 has conditional mean zero. The

estimates in the regression will be biased if any of the variables are correlated with this error term. Figure 6 below shows a scatterplot of the residuals based on the regression model with the price of soybeans as the dependent variable. Although there are some outliers, one could say that the residuals are roughly distributed around the zero line and thus this assumption holds. The results are similar for the regressions of the other three food commodities as dependent variables.

Figure 6: Residuals against fitted values

The second assumption states that the random variables of the model have a stationary distribution. This concerns making sure that the data has been retrieved from a stationary distribution such that the current distribution of the data is equal to the distribution in the past. Section 4.5 will further explain this assumption, the problems nonstationarity poses and will test for this.

-5 0 0 50 R e si d u a ls -100 -50 0 50 100 Fitted values

(23)

23

The third assumption states that large outliers are unlikely. Once the final regression model is specified and estimated and also looking at the data, this is indeed the case.

The final assumption concerns the need for absence of perfect multicollinearity. In case of perfect multicollinearity, estimators coefficients can become unstable. Since Stata automatically eliminates regressors that are a perfect linear function of one of the other regressors, and thus automatically deals with cases of perfect multicollinearity, this assumption holds. The case of imperfect

multicollinearity will be discussed in section 4.4.

4.3 Selecting the lag lengths

This section will proceed with describing the procedure for choosing the appropriate number of lags in the final model. Stock and Watson(2012) describe several criteria by which one can choose the number of lags. In this decision it is required to balance the marginal benefit of including one more lag against the marginal cost of additional uncertainty in the estimation of regression coefficients. If the number of lags included is too low, the model will omit possible important information that is contained in the additional lags. On the other hand, as mentioned, adding too many lags will increase the estimation error in the regression model.

So-called information criteria can be used to decide on the number of lags to include. Two of these criteria are discussed by Stock and Watson (2012): the Bayes information criterion (BIC) which is also named Schwarz (Bayes)information criterion (SIB/SBIC) and the Akaike information criterion (AIC). Even though the AIC estimator of the number of lags is not consistent, it is widely used in practice. In many cases it will estimate a larger number of lags compared to the BIC, but it has been shown that it is better to have too many than too few lags. Therefore, in this model the AIC will be used.

Below is the calculation of the information criteria over the entire sample, that is from January 1980 up to and including July 2015. This shows that the AIC indeed argues for one more lag than the BIC (SBIC in Stata). Following these results, 3 lags of all variables will be included in the final model.

(24)

24

Table 1. Selection-order criteria for total sample (1980-2015)

4.4 Testing for multicollinearity

As mentioned, perfect multicollinearity arises when one of the regressors is a perfect linear combination of any of the other regressors, or in other words, the correlation between these variables is 1. Since Stata automatically corrects for this, this section focuses on the second type of multicollinearity: imperfect multicollinearity.

When variables are highly correlated but this correlation is not equal to 1, we have a case of imperfect multicollinearity. The case of imperfect multicollinearity does not necessarily prevent the estimation of the regression. It does however mean that one or multiple of the regression

coefficients can be estimated imprecisely (Stock and Watson, 2012). Without multicollinearity, the estimation of a regression coefficient can be interpreted as the effect of a one unit change of that variable on the dependent variable holding all other variables constant. If imperfect multicollinearity is present the included regressor variables are highly correlated and therefore it is unlikely to

estimate the effect of an independent change in one of these regressors.

Clearly, imperfect multicollinearity could pose an obstacle in this regression model. The various price variables of the commodities included seem to have very strong linkages when looking at their development over time, such as Figure 1 showed in the introduction. This intuition is further strengthened by looking at the various correlations that are shown below in Table 2.

Table 2. Correlation Matrix

OIL SOY WHEAT MAIZE RICE USX

OIL 1.00 SOY 0.864 1.00 WHEAT 0.872 0.908 1.00 MAIZE 0.852 0.932 0.906 1.00 RICE 0.759 0.800 0.779 0.794 1.00 USX -0.582 -0.579 -0.599 -0.520 -0.561 1.00 Exogenous: _cons

Endogenous: SOY OIL WHEAT RICE MAIZE USX

4 -8528.88 63.574* 36 0.003 2.7e+10 41.0349 41.602 42.4701 3 -8560.67 93.171 36 0.000 2.6e+10* 41.015* 41.446 42.1057 2 -8607.25 337.34 36 0.000 2.8e+10 41.065 41.3599* 41.8113* 1 -8775.92 6946.6 36 0.000 5.2e+10 41.6923 41.8511 42.0942 0 -12249.2 5.9e+17 57.9443 57.967 58.0017 lag LL LR df p FPE AIC HQIC SBIC Sample: 1980m5 - 2015m7 Number of obs = 423 Selection-order criteria

(25)

25

A more formal way to detect the possible problem of imperfect multicollinearity is to test by the Variance Inflation Factor (VIF). The gives an index of how much the variation of one of the estimated coefficients of the regression is increased because of collinearity. A VIF higher than 10 is usually seen as an indicator that multicollinearity is present. Stata automatically also calculates the reciprocal of the VIF (1/VIF). In this case, any value below 0.1 is considered proof of the presence of

4.5 Nonstationarity testing

The following section will deal with the possibility that the variables included in the model are nonstationary. If either the dependent variable or the included regressors are nonstationary, the estimated coefficient of these variables and the accompanying t-statistic can have a nonstandard distribution. This in turn leads to potential unreliable forecasts, hypothesis tests and confidence intervals (Stock and Watson, 2012). The possible issue of nonstationarity will be looked at in two different ways: the possibility of a unit root and the existence of structural breaks in the price of crude oil.

4.5.1 Testing for a unit root

The first possible case of nonstationarity is the existence of a trend, a persistent long-term

movement of a variable over time. In econometrics, the focus lies on so-called stochastic trends, a trend that is random and varies over time. If a stochastic trend is existent, we can say that the series has a unit autoregressive root, or a unit root (Stock and Watson, 2012).

A more formal explanation of a unit root is that in this case the correlation of the current value of a variable with its lagged values is close to 1. If a variable contains a unit root this will mean that the variance of this variable increases over time and the distribution of the variable will also change over

(26)

26

time. In this case the OLS estimator of this regressor and the accompanying t-statistic can have a nonstandard distribution. This will lead to the potential for unreliable forecasts as mentioned above. Three possible problems can arise from the existence of a unit root. Firstly, the estimator of the coefficient of the first lag of the dependent variable can be biased towards 0 when the true value is in fact 1. Also, the t-statistic on a particular regressor can have a nonnormal distribution. Finally, the existence of a unit root can cause two series that are actually independent to wrongfully appear to be related, a problem that is called spurious regression (Stock and Watson, 2012). To assure these problems do not arise, testing for unit roots is required.

According to Stock and Watson (2012), both an informal and a formal way can be used to detect the presence of a unit root. The informal way focuses on the autocorrelation coefficient of the series. More precisely, computing the first autocorrelation (that is, the correlation of a variable with its first lagged value) will provide a first proof of the existence of a unit root. As mentioned above, a unit root is present if this first autocorrelation is close to 1. In the case of this model, we will thus be looking at the correlation of the variables included with the value of that same variable in the previous month. The table below provides autocorrelations for the first three lags of the included variables.

Table 3. Autocorrelations

OIL SOY WHEAT MAIZE RICE USX

First lag 0.9919 0.9847 0.9816 0.9863 0.9794 0.9939 Second lag 0.9774 0.9600 0.9543 0.9659 0.9424 0.9839 Third lag 0.9604 0.9326 0.9282 0.9423 0.9068 0.9735

Unsurprisingly, looking at the values of the first autocorrelation it shows that all series do seem to have a unit root and are thus nonstationary. Especially for the US Dollar exchange rate and the crude oil price, with values above 0.99, this is very clear.

To ascertain that we indeed are dealing with series containing a unit root, we now turn our attention to a more formal way of testing for the existence of a unit root. Several possibilities exist, and the paper by Chen et al. (2010) uses the Augmented Dickey-Fuller test and the Phillips and Perron test. In this section however, the so-called DF-GLS test will be used. This test was developed by Elliot, Rothenberg and Stock in 1996. According to Stock and Watson (2012) the ADF test is the most commonly used test in practice and was also the first test developed to test the null hypothesis of a unit root. The DF-GLS test is similar to ADF test, apart from the fact that the time series under investigation is first transformed via a generalizes least squares regression before the test is

(27)

27

performed. In their article presenting this enhanced test, Elliot et al.(1996) argue the case that the DF-GLS test shows an improvement over the ADF test in terms of power. This means that it will more likely reject the proposed null hypothesis of a unit root against the alternative hypothesis that the series is stationary, when in reality the latter is the case. It is thus better at distinguishing between an actual unit root, where autocorrelation is 1, and a root that is large but less than 1. Elliot et al.(1996) show that this is especially the case when an unknown time trend is present.

The DF-GLS test for a unit autoregressive root tests the null hypothesis that a series contains a unit root against the one-sided alternative that this is not the case. Rejection of the null hypothesis thus states that there is no presence of a unit root. The DF-GLS test can both be done with including a time trend, or excluding this time trend. In the first case, the null hypothesis is tested against the alternative hypothesis that the variable in question is stationary around a deterministic linear time trend. The second case tests against the alternative that the variable is stationary with a mean that can be nonzero, but does not follow a time trend (Stock and Watson, 2012).

Table 5 shows the results for the DF-GLS Test for the variables included. The number of lags is selected using the Ng-Perron approach. Combining this table with the critical values given in Stock and Watson (2012) as reproduced in Table 6, we can see that, at the 5% significance level, only the null hypothesis for USX cannot be rejected in the case of excluding a trend. Including a trend, none of the null hypotheses can be rejected. There thus is strong evidence of non-stationarity in all variables included.

If a series has a unit root, then the first difference of this series does not have a unit root. An effective way of mitigating the problems of non-stationarity is thus transforming the included variables into first differences. In the final model specification, first differences of all variables will therefore be used.

Table 5: Results of the DF-GLS Test

Lags No trend Including trend

OIL 13 -1.164 -1.399 SOY 11 -1.648 -2.315 WHEAT 12 -1.940 -2.205 MAIZE 16 -1.736 -2.623 RICE 13 -1.698 -1.769 USX 10 -2.027 -2.262

(28)

28

Table 6: Critical Values of the DF-GLS Test

10% 5% 1%

No trend -1.62 -1.95 -2.58

Including trend -2.57 -2.89 -3.48

4.5.2 Testing for structural breaks

A second type of nonstationarity arises in the case where a certain time series shows structural changes, for example a shift in the mean level of the series over time. These changes are called breaks, and ignoring these breaks will cause a regression model to estimate and forecast on the basis of misleading information. The OLS estimator will focus on estimates of a relationship that hold on average over the whole time period investigated. This average could however be significantly different from the true regression function for a subset of the period described, thus leading to poor estimation. Breaks can arise due to several causes, such as a change in macroeconomic policy, changes in the structure of the economy or an innovation that has a large impact in a certain industry. Apart from these almost instantaneously, discrete breaks, breaks can also occur more slowly. This could for example be due to slow evolution of economic policy and ongoing changes in the structure of the economy (Stock and Watson, 2012).

The graph below shows once again the evolution of the oil price over time using data from the IMF Cross Country Macroeconomic Statistics with an added linear trend line. The graph shows that over the 35-year period investigated, the average level of the crude oil price greatly differs. Up until 2004 it moved between the ranges of around 10 and 40 US dollars a barrel. Starting in 2004 however the price of crude oil experienced enormous growth, both in its level as in its volatility.

(29)

29

Source: IMF Cross Country Macroeconomic Statistics

Chen et al. (2010) find several structural breakpoints in the movement of the price of oil. One of the structural breakpoints they find is by observing the data. From this they conclude that week 20 of 2008 (they use weekly data) can be considered as a structural break since this is the highest peak of the oil price. Indeed, also in the sample used in this thesis one could argue that July 2008 is a

structural breakpoint, since prices rapidly go down after this peak month. Chen et al. (2010) continue the investigation of structural breaks by performing the two-break minimum Lagrange Multiplier unit root test for the total time frame preceding week 20 of 2008. Hereby they find another two

breakpoints: week 49 of 1985 and week 3 in 2005, which correspond to November 1985 and January 2005 using monthly data as this thesis does. After finding the above mentioned breaks, Chen et al.(2010) continue their estimation of the final model for four separate sub-periods.

This section will proceed by testing whether the breakpoints found by Chen et al.(2010) are also considered breakpoints in this data set. A Chow test will be conducted to see if November 1985, January 2005 and July 2008 are indeed structural breaks in the price of crude oil. The Chow test tests whether the coefficients estimated in the period before the breakpoint under consideration are equal to the coefficients over the months afterwards. In other words, it tests whether there are discrete changes in the regression coefficients.

The procedure of testing for breaks will be explained below, using November 1985 as an example of a suspected breakpoint. First of all, a dummy variable will be generated that equals the value of 0 whenever we are in the time period before November 1985 and 1 in case we are at a later point in

0

𝑂𝐼𝐿

𝑡

_𝑡

_𝑙=1𝑇

Ω

₁

𝑈𝑆𝑋

_𝑡−𝑙

+ 𝑢

_𝑡

This regression model is identical to the one described in section 4.1 apart from the terms that include 𝐷𝑡(𝜏). In this model 𝐷𝑡(𝜏) is the dummy variable which will equal 0 if t is smaller or equal to

the hypothesized break date τ. In the case that the coefficient on OIL and its lagged values do not greatly differ before and after the hypothesized break, ∆1= ∆2= ∆3= 0 and the interaction terms

will drop out. The population regression function will then be the same both before and after the break and the hypothesized breakpoint can then be rejected. The hypothesis of a break can thus be tested by the F-statistic that tests ∆1= ∆2= ∆3= 0 against the alternative that at least one of these

coefficients is nonzero. This is called the Chow test (Stock and Watson, 2012). After construction of the dummy term and interaction terms with OIL and its first three lagged values are set up, the full regression is estimated. Lastly, an F-test is conducted on the estimation coefficients of the dummy and the interaction terms. Appendix 2 shows this regression and the Chow test statistic. In this case, we conclude that there is not enough evidence to reject the null hypothesis of no break. This test was however done with SOY as the dependent variable, so the same procedure has to also be done for the other three food commodities as the dependent variable. Redoing this procedure for all commodities and for all three hypothesized breakpoints gives the tables with F-statistics and p-values as given in Appendix 3. From these tables it can be inferred that within this sample, only July 2008 is found to be a breakpoint. To account for this break in the final model, the sample will thus be split up into two periods: January 1980 up to and including July 2008 and August 2008 up to and including July 2015.

(31)

31

4.6 Testing for heteroscedasticity

Lastly, this section will test for heteroscedasticity. If the variance of the conditional distribution of the error term in the model is constant and does not depend on the independent variables, the error term is homoscedastic. If this is however not the case, heteroscedasticity is present. In case of homoscedasticity, homoscedasticity-only standard errors can be used while computing the t-statistic, which is also the default setting in Stata. Using homoscedasticity-only standard errors while in reality the error term is heteroskedastic will result in non-normal distributed t-statistics. This will affect the validity of confidence intervals: the probability that a confidence interval of 95% will indeed contain the true value of the coefficient is not 95%. It is worth mentioning that the OLS-estimators

themselves remain unbiased, consistent and asymptotically normal, whether the errors are homoscedastic or heteroskedastic (Stock and Watson, 2012).

A formal test to check for heteroscedasticity is the Breusch-Pagan/Cook-Weisberg test, a test that is included in Stata. This will test the null hypothesis of a constant variance of the error term, that is homoscedasticity, versus the alternative that heteroscedasticity is present. Appendix 4 shows the results of the Breusch-Pagan/Cook-Weisberg test both for the entire time period of the data set and for the two separate time periods as found in section 4.5.2. An example for all three of these tests, taking SOY as the dependent variable, is also given in Appendix 4. Utilizing this test for all four food commodities in the three different time periods gives the table with test statistics and p-values which can also be found in this appendix. It clearly shows that, given the high values of the test statistic, the null hypothesis of homoscedasticity is rejected when the entire time period is investigated and for the subset of period 1. For period 2 however, the null hypothesis is not rejected. This implies that to mitigate any problems with the validity of t-statistics and confidence intervals in the final model estimation, it is appropriate to use heteroscedasticity-robust standard errors for regressions run in period 1. For period 2, the standard assumption of homoscedasticity is found to be appropriate.

4.7 Final specification of the model

This section will conclude chapter 4 by specifying the final model that will be utilized to estimate the dynamic relationships of this model. Starting from the model outlined in section 4.2 we have the following:

𝑆𝑂𝑌

_𝑡

= 𝛼

₀

+ ∑

𝑇_𝑙=1

𝛼

₁

𝑆𝑂𝑌

_𝑡−𝑙

+ 𝛽

₀

𝑂𝐼𝐿

_𝑡

+ ∑

𝑇_𝑙=1

𝛽

₁

𝑂𝐼𝐿

_𝑡−𝑙

+ 𝛾

₀

𝑊𝐻𝐸𝐴𝑇

_𝑡

𝑙=1𝑇

Ω

1

𝑈𝑆𝑋

𝑡−𝑙

+ 𝑢

𝑡

(32)

32

To counter the problems arising from the presence of unit roots in all series, all of the variables included will be converted into first differences. Moreover, since July 2008 was found to be a

structural break in the price of oil, the model will be estimated for two distinct periods: January 1980 up to and including July 2008 and August 2008 up to and including July 2015. To mitigate the

problems of heteroscedasticity, all regressions performed for the first period will we done so with heteroscedasticity-robust standard errors. The next chapter will continue by estimating the models and analyzing the results.

Oil price spillovers : analysing the effect of oil price changes on four major grains using an ARDL-Model