UNIVERSITY OF NOTTINGHAM
SCHOOL OF ECONOMICS
MSc DISSERTATION
L14100
Investigating the Long Run Relationship Between
Crude...
1
2
ABSTRACT
Crude oil price is believed to be one of the factors that affect food commodity prices. It is an
agricultural p...
3
4
CONTENTS
1. Introduction 6
2. Fundamentals 9
3. Literature Review 11
4. Data 13
5. Methodology 15
6. Empirical Results a...
5
6
1. INTRODUCTION
Food prices have been very volatile in the most recent years, reaching peak levels in 2008 and then
decl...
7
On the supply side, with increase in crude oil prices, it pushes up crop production cost and which
results in grain pric...
8
prices, which as a result will hurt consumers. Hence, it is very important that food prices remain
stable. However, the ...
9
2. FUNDAMENTALS
In this section, I will discuss the factors which are commonly assumed to be responsible in driving
food...
10
SUPPLY SHOCKS
Adverse weather and crop diseases have played a significant role in reduced crop production and
thereby l...
11
3. LITERATURE REVIEW
The attempts to examine the long term relationship between crude oil prices and food commodity
pri...
12
Chen et al. (2010) too investigated the relationships between the crude oil price and the global grain
prices for the t...
13
4. DATA
The period chosen for this study extends from January 1980 to December 2011 and comprises of
(32 x 12) = 384 mo...
14
All the prices of the commodities are in their nominal rates. The length of the period is long enough
to determine the ...
15
5. METHODOLOGY
In this paper we will use a simple model to estimate the relationship between petroleum prices and
price...
16
The ADF test can be tested on at least three possible models:
i) A pure random walk without a drift. It is defined by u...
17
5.2 CO-INTEGRATING TEST
The two most commonly used approaches to find long-run relationship between variables are the
E...
18
Now to test the hypothesis on to determine whether the residuals are stationary, we will follow:
Firstly, we set the Nu...
19
A simple dynamic model of a short-run adjustment model is given by:
(1.5)
where is the dependent variable, is the indep...
20
Next, we will carry out a few diagnostic tests on the model obtained in order to determine if it
satisfies a few assump...
21
a) NORMALITY TEST
We will use the Jarque-Bera normality test is used to determine whether the residuals in the Error
Co...
22
c) HETEROSCEDATICITY TEST
Heteroscedasticity results from a sequence of random variables having differing variances, i....
23
The Causality relationship can be evaluated by estimating the following linear regression models. For
illustration, con...
24
6. RESULTS AND ANALYSIS
The results of this paper are summarized in this section. This study used time series data for ...
25
However, the null hypothesis was rejected for all the variables in their first differences, which
implies that the seri...
26
statistic measures the success of the regression in predicting the values of the dependent variable
within the sample. ...
27
ADF regression discussed in the methodology section. The residual ADF statistic is called the Engle-
Granger ‘tau’ stat...
28
Note: Numbers in parentheses under the coefficients are standard errors &
The test results are in Appendix 2.4
MAIZE
AD...
29
which is used as a feedstock for biodiesel production. Therefore, another crop whose prices can
be affected because of ...
30
models, we will estimate our ECM. The methodology for setting the up the model has been discussed
in the methodology se...
31
Table 3 summarizes the coefficient estimates obtained from the Error Correction Models. Firstly, we
can see that the si...
32
Table 4. GRANGER CAUSALITY TEST
Commodity Hypothesis F-
Statistics
p-value Causal
Reference
Crude oil (lnp)
& Maize (ln...
33
7. CONCLUSION
The motivation to work on this topic was mainly to learn about the nature of the rise in prices of
agricu...
34
BIBLIOGRAPHY
Yu, Tun-Hsiang, D.A. Bessler, and S. Fuller. (2006). “Cointegration and Causality Analysis of
World Vegeta...
35
Chen, S.T., Kuo, H.I., Chen, C.C., (2010). “Modelling the relationship between the oil price and
global food prices.” A...
36
APPENDIX
UNIT ROOT TEST
1) lnp
Null Hypothesis: LNP has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Au...
37
2) d(lnp)
Null Hypothesis: D(LNP) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=1...
38
3) lnm
Null Hypothesis: LNM has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic - based on SIC, ...
39
4) d(lnm)
Null Hypothesis: D(LNM) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=1...
40
5) lnr
Null Hypothesis: LNR has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 2 (Automatic - based on SIC, ...
41
6) d(lnr)
Null Hypothesis: D(LNR) has a unit root
Exogenous: Constant
Lag Length: 1 (Automatic - based on SIC, maxlag=1...
42
7) lns
Null Hypothesis: LNS has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic - based on SIC, ...
43
8) d(lns)
Null Hypothesis: D(LNS) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=1...
44
9) lnw
Null Hypothesis: LNW has a unit root
Exogenous: Constant, Linear Trend
Lag Length: 1 (Automatic - based on SIC, ...
45
10) d(lnw)
Null Hypothesis: D(LNW) has a unit root
Exogenous: Constant
Lag Length: 0 (Automatic - based on SIC, maxlag=...
46
2. CO-INTEGRATION TEST (ENGLE-GRANGER TWO STEP METHOD)
2.1 STATIC REGRESSION EQUATION FOR WHEAT
Dependent Variable: LNW...
47
F-statistic 3154.277 Durbin-Watson stat 1.455045
Prob(F-statistic) 0.000000
2.3
a) MAIZE
Cointegration Test - Engle-Gra...
48
Engle-Granger z-statistic -30.18080 0.0057
*MacKinnon (1996) p-values.
d) WHEAT
Cointegration Test - Engle-Granger
Date...
49
b) SOYBEANS ADL(1)
Dependent Variable: LNS
Method: Least Squares
Date: 09/19/12 Time: 01:29
Sample (adjusted): 1980M02 ...
50
3. ERROR CORRECTION MODEL
1) MAIZE
Dependent Variable: D(LNM)
Method: Least Squares
Date: 09/12/12 Time: 19:49
Sample (...
51
Prob(F-statistic) 0.002114
3) WHEAT
Dependent Variable: D(LNW)
Method: Least Squares
Date: 09/12/12 Time: 19:54
Sample ...
52
Prob(F-statistic) 0.000124
4. GRANGER CAUSALITY TEST
1) MAIZE
Pairwise Granger Causality Tests
Date: 09/12/12 Time: 19:...
53
LNW does not Granger Cause LNP 1.23447 0.2922
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Investigating the Long Run Relationship Between Crude Oil and Food Commodity Prices

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"Crude oil price is believed to be one of the factors that affect food commodity prices. It is an
agricultural production input, therefore the prices of fertilizer, fuel and transportation are affected by the crude oil prices directly, and subsequently they influence the production of grain commodities. There is another dimension to how oil prices can affect food commodity prices, and it is from the derived demand for biofuels. With rising oil prices, demand for biofuels increase and the production
of these fuel is highly dependent on the availability of agricultural feed stocks. So it is primarily because of the above two dynamics that I want to investigate if there is a long term relationship between crude oil prices and food commodity prices. This is an important issue in present times because of the rising prices and volatility in the oil and food commodity markets. I will try to examine if there exist a cointegrating relationship between crude oil price and food commodity price for the period between 1980 to 2011. The food commodities selected are maize, rice, soybean and wheat. Time Series econometric techniques were applied to find our results. The Engle-Granger Co-integration test revealed that there is long run relationship between crude oil prices and maize, soybean, wheat. But, rice prices were not found to be cointegrated. I also carried out the traditional Granger Causality test to check whether causality exist between the two prices. We find that there is unidirectional causality, with only crude oil prices ‘Granger causing’ each of the four food commodity prices. The reverse was not true, as crude oil prices were not found to be influenced by price of food commodities. So from our results we can confirm the significance of oil prices and the impact it has on the food commodity prices."

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Investigating the Long Run Relationship Between Crude Oil and Food Commodity Prices

  1. 1. UNIVERSITY OF NOTTINGHAM SCHOOL OF ECONOMICS MSc DISSERTATION L14100 Investigating the Long Run Relationship Between Crude Oil and Food Commodity Prices Submitted by: ABHISHEK GOGOI 4164241 MSc Economic Development and Policy Analysis. Supervisor: Dr. Marta Aloi. “This Dissertation is presented in part fulfillment of the requirement for the completion of an MSc in the School of Economics, University of Nottingham. The work is the sole responsibility of the candidate”
  2. 2. 1
  3. 3. 2 ABSTRACT Crude oil price is believed to be one of the factors that affect food commodity prices. It is an agricultural production input, therefore the prices of fertilizer, fuel and transportation are affected by the crude oil prices directly, and subsequently they influence the production of grain commodities. There is another dimension to how oil prices can affect food commodity prices, and it is from the derived demand for biofuels. With rising oil prices, demand for biofuels increase and the production of these fuel is highly dependent on the availability of agricultural feed stocks. So it is primarily because of the above two dynamics that I want to investigate if there is a long term relationship between crude oil prices and food commodity prices. This is an important issue in present times because of the rising prices and volatility in the oil and food commodity markets. I will try to examine if there exist a cointegrating relationship between crude oil price and food commodity price for the period between 1980 to 2011. The food commodities selected are maize, rice, soybean and wheat. Time Series econometric techniques were applied to find our results. The Engle-Granger Co-integration test revealed that there is long run relationship between crude oil prices and maize, soybean, wheat. But, rice prices were not found to be cointegrated. I also carried out the traditional Granger Causality test to check whether causality exist between the two prices. We find that there is unidirectional causality, with only crude oil prices ‘Granger causing’ each of the four food commodity prices. The reverse was not true, as crude oil prices were not found to be influenced by price of food commodities. So from our results we can confirm the significance of oil prices and the impact it has on the food commodity prices.
  4. 4. 3
  5. 5. 4 CONTENTS 1. Introduction 6 2. Fundamentals 9 3. Literature Review 11 4. Data 13 5. Methodology 15 6. Empirical Results and Analysis 24 6.1 Augmented Dickey Fuller Unit Root test 6.2 Co-integration Analysis 6.3 Short-run Analysis: Error Correction Model 6.4 Causality test 7. Conclusion 33 Bibliography 34 Appendix 36
  6. 6. 5
  7. 7. 6 1. INTRODUCTION Food prices have been very volatile in the most recent years, reaching peak levels in 2008 and then declining sharply but to rise again in 2010. Figure 1 shows the monthly price indices from January 2000 until May 2011, and it illustrates the evolution of the various agricultural food commodity prices over this period. The 2008 commodity price boom was one of the broadest and it did receive a lot of attention all over the world. As food commodity prices were reaching very high levels, it raised questions about the factors causing this hike and breaking the price stability that was continuing for the previous 10 to 15 years. Between January 2006 and March 2008, food commodities on average underwent an increase of 62%, amongst which rice prices being the most notable; with prices doubling within just five months of 2008, from US $375 per tonne in January to US $757 per tonne in June (IMF, 2008). Soon after reaching peak, there was a rapid decline in the prices. But by 2011, the prices of maize (corn), soybeans and wheat returned to their peak levels of 2008. This amplitude of price movements over a particular period of time has been at its highest level in the past 50 years and it asks many questions with regard to the causes of this price volatility. One interesting feature in the figure below is the trend of the commodity prices. Does it appear that the spikes in the prices of crude oil are of a similar trend to those of the commodity prices (especially during the 2007-09 period)? In recent years, crude oil prices have escalated to record levels, peaking at US $133 per barrel in July 2008. It is understood that among the various factors that affect agricultural commodity prices, crude oil prices is one element that plays an important role. Figure 1: Monthly Agricultural Commodity Prices, 2000-2011 Note: Monthly commodity prices are expressed as an index equal to 1 on average in 2002. Source: IMF, 2011
  8. 8. 7 On the supply side, with increase in crude oil prices, it pushes up crop production cost and which results in grain price increase. (Baffes J, 2007) indicated that the crude oil price should be included in the aggregate production function for most primary agricultural commodities through the use of various energy-intensive inputs. For instance, the prices of fertilizer, fuel, and transportation were found to be affected by the crude oil price directly and subsequently influenced the production of grain commodities. Then on the demand side, grain commodities are competing with the derived demand for bio-fuels. With rising fuel prices, governments are taking steps to increase plantation of energy crops (eg. maize) by providing generous subsidies. Therefore, larger and larger share of maize production is being used to produce biofuels, partly as a substitute to petroleum. As a result, they strengthen the link between the two markets- crude oil and of the agricultural products used in production of biofuels. So we can see how the two sectors are related and it is on this topic that I will try to investigate if there exist a long term relationship between crude oil prices and the selected food commodities. An important discussion with regard to the the linkages between crude oil and the food commodity markets, is the question regarding the food and energy issue. “The Food Versus Fuel Debate”, was the title of the August 2009 issue of Journal of Agriculture and Applied Economics and this heading hits the focal point of the discussion. We live in a world that is thirsty for energy but at the same time, there is concern about the long term sustainability of this energy-intensive lifestyle that the industrialised world has developed. Oil reserves are being exhausted and at the same time there is increasing demand for energy from economies to fulfill their growing needs. With rising oil prices and also growing environmental concerns, there is a call for finding alternatives, and biofuels is leading the way in this new direction. The European Union, the United States and other major agricultural production countries have all been encouraging biofuels by implementing production subsidy and setting mandates to encourage farmers to plant energy crops. The farmers are complying with these mandates by diverting agricultural land to producing energy crops. For example, in 2007 the US diverted more than 30 per cent of its maize production, Brazil used half of its sugarcane production and the European Union used the greater part of its vegetable oil seeds production as well as imported vegetable oils, to make biofuel. So is this the new measure of meeting our energy needs, by diverting crop and land away from traditional use to non-food use? Another question attached to this is whether the increase in biofuel crops is affecting other food crop prices. There are a few studies that find significant effects of biofuel prices on agricultural commodity prices. Roberts and Schlenker (2010) estimate the impact of United States biofuel production alone on world prices of maize, rice, soybeans and wheat to be about 30 per cent. The world faces a new food economy that most likely involves higher and more volatile food prices, as we are seeing in recent years. High food prices lead to either spending more money on food purchases or making cutbacks on the quantity or quality of food. It definitely makes an impact and especially on poorer households who get most affected. There is also broad agreement among policymakers that food commodity price hike brings inflation risk that could spill into expectations for further price increases, demand for higher wages and thereby an increase in underlying inflation (second-round effects). Along with the high prices, price volatility too has significant effects on food producers and consumers. Producers can be affected with greater potential losses, with price changes that are larger and faster to what they can adjust. It is a big problem because uncertainty about prices make it more difficult for farmers to make sounds decisions about ‘how’ and ‘what’ to produce. It will make them more cautious and may also prevent them from making investments in areas that can improve productivity. Subsequently there will be reductions in supply and this could lead to higher
  9. 9. 8 prices, which as a result will hurt consumers. Hence, it is very important that food prices remain stable. However, the prices of the recent years have been quite the contrary and it leads to questions about the ‘causes’ of this food price volatility. Despite the differences in views among economist, it is commonly assumed that there are a few causes, which I will discuss in the following section. But among which, Oil Prices is one key element. It is on this topic that I will try to establish if there is a long-run relationship between crude oil prices and food commodity prices, using the Engle-Granger Co-integration test (two-step method). A traditional Granger Causality test will also be used to check whether one price ‘Granger causes’ the other. This paper is organized as follows. In Section 2, I will discuss the factors which are commonly assumed to be responsible in driving food commodity prices. Section 3 is the Literature Review, where I will briefly summarize the existing literature on this topic. Section 4 is the introduction to the Data followed by Section 5 where I will explain the econometric methodology that I will be using to carry out my empirical tests. In Section 6 I will present and analyze the results. Finally, I will conclude in the last section.
  10. 10. 9 2. FUNDAMENTALS In this section, I will discuss the factors which are commonly assumed to be responsible in driving food commodity prices. We will examine the contribution of each of the factors and the role it played in the recent price developments. Agricultural commodity prices have been rising since 2002 and increasing sharply from 2007.The rise in food commodity prices was led by cereals, where from January 2005 until June 2008, maize prices almost tripled, wheat prices increased 127 percent and rice prices increased 170 percent (Mitchell 2008). This was then followed by increases in fats and vegetable oil prices. So the factors that contributed to the rise in the food commodity prices are: MACROECONOMIC DEVELOPMENTS Macroeconomic forces like declining US $ exchange rates and real interest rates are believed to be key factors in the rise in commodity prices; the latter also leading to wave of speculation which causes short-run price rise. The exchange rate was identified by many analysts as one of the key factors in explaining the high commodity prices of 2008. In 2002, a Euro cost US$ 0.90 and when the dollar was weakest in mid-2008, an Euro cost nearly US$ 1.60. A weak dollar means commodity prices seem less expensive for those countries whose currencies have appreciated relative to the dollar, so it may lead to increased demand and thereby exert price pressures. Statistical analysis has shown that the depreciation of the dollar increases dollar commodity prices on average with an elasticity between 0.5 and 1.0 (Gilbert 1989; Baffes 1997). Using an elasticity of 0.75, about 15 percent of the recent increase in agricultural commodity prices can be attributed to the decline of the U.S. dollar (Mitchell 2008). A weak dollar, inflationary expectations and economic recovery are factors that have led to “financialization” of commodity markets, and there have been increased investment in commodities by institutional investors wanting to diversify their portfolios. This financialization is often thought to have affected commodity price behaviour. Another view shared is that these prices are largely driven by speculators and herd behaviour among investors looking for alternative asset classes. The low interest rates that were supported by the central banks resulted in excess liquidity, which too made their way to the commodity markets. FUNDAMENTAL CHANGE IN AGRICULTURAL SUPPLY AND DEMAND With rising world population there is an increased demand for grain. A big factor for this increased demand is because of the emerging economies and their dietary changes with income growth. As incomes per head rise in countries like China and India, there has been a structural shift in their demand for grain and their consumption patterns are changing. There is a rise in meat consumption and as a result of which, there is more demand for animal feeds. Between 1995 and 2005, world meat consumption rose by 15 per cent, East and Southeast Asia being the region with the highest increase at almost 50 per cent (FAO,2009). There has been increased oilseed demand and higher oilseed prices as China increased soybean imports for its livestock and poultry industry. On the Supply side, both China and India have been net grain exporters since 2000, although exports have declined as consumption has increased (Mitchell 2008).
  11. 11. 10 SUPPLY SHOCKS Adverse weather and crop diseases have played a significant role in reduced crop production and thereby leading to reductions in the inventories in 2010-11. World total grain production dropped 2.3% or 51 million metric tonne in 2010-11 from the previous year (USDA). These large reductions were largely caused as a result of harmful weather in the Black Sea Region, Canada and Australia. With reduced production, governments take policy actions such as increased taxes or export bans which lead to higher prices. HIGHER OIL PRICES The increase in oil prices have a two-fold effect on crop prices. On the supply side, with increase in crude oil prices, it pushes up crop production cost with relation to higher fertilizer, chemicals and transportation costs; thereby resulting in grain price increase. On the demand side, grain commodities are competing with the derived demand for bio-fuels. With rising fuel prices, governments are taking steps to increase plantation of energy crops (eg. maize) by providing generous subsidies, and the farmers are complying with these mandates by diverting agricultural land to producing energy crops. This as a result is not only leading to reduced food productions but also affecting food prices. For example, growing biodiesel production in Europe has indirectly exacerbated price rises in the wheat market, because land which would otherwise have been used for growing wheat has been diverted to oilseed production (Mitchell, 2008).A recent study by UNCTAD (2009) estimates that, due to blending requirements in many countries, demand for biofuels will rise much faster than production capacity. In addition, with subsidized biofuel prices, it implies that biofuel production has zero elasticity with respect to changes in feed prices. Therefore it seems plausible that enhanced biofuel production will have some effect on maize prices and also on the prices of other grains such as barley, rice and wheat via the substitution effect. There are a few studies that find significant effects of biofuel prices on agricultural commodity prices. Roberts and Schlenker (2010) estimate the impact of United States biofuel production alone on world prices of maize, rice, soybeans and wheat to be about 30 per cent. However, there are also several other studies which don’t quite agree to this idea that biofuel prices can have a serious impact on food commodity prices. Baffes and Haniotis (2010) say that it is highly unlikely that biofuel production prompted the recent agricultural commodity price spikes, given the small share of land used for biofuels compared to global land used for grain and oilseed production. POLICY RESPONSES International trade is a mechanism by which countries adjust to production and demand shocks. But when food prices increased in 2007-08, countries altered trade policies to isolate and partially stabilize their domestic markets from effects of those high prices. Countries use various measures such as subsidise food prices, decreased taxes or decreased import tariffs. But the measure that was mostly used was export restrictions. But each of the policy actions only fuel the price increase even further by either restricting access to supplies (with export restrictions) or by increasing demand for product (with subsidies). Hence, even if countries take policy measures to shield the domestic market, the outcome will be self-defeating if all countries take the same measures. An example of the impact these bans have is exemplified by how Thailand’s rice export price skyrocketed after India banned rice exports in October, 2007. Export markets for main staple commodities are concentrated in a few countries and if they restrict exports, it immediately affects global prices.
  12. 12. 11 3. LITERATURE REVIEW The attempts to examine the long term relationship between crude oil prices and food commodity prices is relatively new, as this topic grabbed attention prominently only during the 2008 food price crisis. Almost all the studies on this topic were inspired post the fuel and food price hike in 2008. In present times, issues related to commodity markets are quite common. Indeed there is no day when daily financial newspapers do not dedicate columns to commodity related issues, from gold to wheat, rice and maize; while an unprecedented rise in oil prices has inflamed all markets (Geman, 2005). It is well documented that food commodity prices are dependent on various factors, among which crude oil price is an important element. With rising fuel prices, there is incentive to use food crops for producing biofuel energy. But increased food production expenditure is not adding up to more food available for traditional use and consequently increasing food prices around the word (Von Braun and Pachauri, 2006). There is a very interesting inter-dependence between the two markets, but is there a long term relationship between the two? There are studies that attempted to examine this relationship and there have been varied results. Arshad and Hameed (2009) carried out a study to investigate whether or not there is a long-term relationship between petroleum and cereal prices using monthly data over the period of January 1980 to March 2008. The bivariate co-integration approach using the Engle-Granger two stage estimation procedure was applied and the results showed evidence of long-run equilibrium relation between the two prices. The Granger causality test was also carried out to test the causality between the variables and the results revealed a unidirectional long run causality from petroleum price to cereal prices. They go on to add that petroleum price is a factor growing in significance in the cereal complex. As an aggregate production input, we know that rising fuel cost will push cereal production cost up. However, there is another dimension to this linkage as with rising oil prices, there is increasing demand for biofuels. As crude oil prices get higher, there is more demand for energy crops such as maize- which is a feedstock to producing biodiesel. So with increasing maize production, maybe by switching crop from wheat to maize or another possibility of more maize production for biofuel use rather than traditional use. All this is bound to change the dynamics of the cereal market and affect food commodity prices. Therefore we can see the greater significance oil price has on the cereal prices. Campiche et al. (2007) examined the evolving correspondence between petroleum prices and agricultural commodity prices, especially keeping in mind the changing dynamics of the energy sector as production of renewable fuels have increased dramatically. The aim was to analyze the co- variability between crude oil prices and the following commodities- corn, sorghum, sugar, soybeans, soybean oil and palm oil. Weekly data was used for the period 2003-07 and they tried to investigate the co-integration between variables by running a vector error correction model, as it considers both the long-run and short run relationships among variables. The Johansen co-integration test was carried out for two periods 2003-05 and 2006-07. The co-integration tests revealed cointegration of corn and soybean prices with crude oil but only during the 2006-07 period. Their results also indicate that the crude oil prices do not adjust to the changes in corn and soybean market. They go on to say that renewable fuels industry will continue to grow strongly and has the potential to positively affect many agents in the US economy. However, new opportunities will also bring new sources of risk as the agricultural food commodity markets may become more dependent on the crude oil market.
  13. 13. 12 Chen et al. (2010) too investigated the relationships between the crude oil price and the global grain prices for the three food commodities- corn, soybean, and wheat. The time period covered in this study extends from the 12th week in 1983 to the 5th week in 2010. The time period was divided into further three sub-periods mainly because the data for crude oil price varies during different periods and therefore two breakpoints were found in the 49th week in 1985 and the 3rd week in 2005. So in all there were four periods. The empirical results showed that change in each grain price was significantly influenced by the changes in crude oil and other grain prices during the third period, extending from (2005w03 to 2008w20). The unique feature of this study is that the relationships are determined using an Autoregressive distributed lag (ARDL) model. So the price of grain was explained by lags of its own price; the current and lag price of oil; and the lag prices of the other two grain prices. Therefore, it not only examines if oil prices affect the grain prices but also considers the effect other food commodities (eg. Soybean and Wheat) have on Maize. The empirical findings reveal that the change in one grain price was significantly influenced by the changes in other grain prices in the third (2005w03–2008w20) and fourth (2008w21–2010w05) periods. This finding is consistent with the observation that grain commodities are competing with the derived demand for bio-fuels by using soybeans or corn to produce ethanol or bio-diesel. They also find in their results that changes in oil prices lead to changes in grain prices and the results are statistically significant in the first (1983w12-1985w48), third (2005w03–2008w20), and fourth (2008w21–2010w05) periods. This implies that the oil price is the important factor of production cost for grain commodities and intensifies the competition relationships between alternative grains. The three papers we discussed, all found long-run relationship between crude oil and food commodity prices. However, the existing literature on this topic is varied and there are studies that did not get the same findings. One of them being Zhang and Reed (2008) who tried to investigate the dynamic effect of crude oil prices on feed grain prices and pork prices. The authors try to study the cause of rising pork prices in China from a different angle. China’s economist underline the concern if it is the rising crude oil prices and the large scale ethanol production which is responsible for the high pork prices. High feed grain price is believed to be the key element behind rising pork prices. And the feed grain prices are high because with rising fuel prices, there is increased production of biofuel which mainly uses corn and soybean. As a result, biofuel production is driving up the costs of corn and other feed grains which contribute to the rise in pork prices. However, their findings didn’t support the above theory. Their results revealed that crude oil price is not the most influential factor for the rise in feed grain prices and pork prices. It is rather the demand and supply market mechanism which is responsible for this rise. But the author acknowledges that although crude oil prices appeared insignificant over the study period of 2000-07, it will have an impact on food prices as prices keep increasing because of the costs involved and the dynamic relationship with biofuels. The findings of Esmaeili and Shokoohi (2010) were similar to the above author, who indicate no direct long-run price relation between oil and agricultural commodity prices. Yu et al. (2006) examined the relationship between crude oil prices and vegetable oils (soybean, rapeseed, sunflower and palm oil). Their results did not find crude oil prices to have any effect on vegetable oil prices. And the author concludes with the end note that possibly the influence of crude oil price on edible oils will grow if high oil prices continue and edible oils become an increasing source of biodiesel. Additional studies have also examined the relationship among various vegetable oils- (In and Inder, 1997) found a long-run relationship, while (Owen et al., 1997) did not observe a strong enough relationship. And finally, (Ghaith and Awad, 2011) who found long-term relationship between the prices of crude oil and food commodities- maize, wheat, sorghum, soybean, barley, linseed oil, soybean oil and palm oil.
  14. 14. 13 4. DATA The period chosen for this study extends from January 1980 to December 2011 and comprises of (32 x 12) = 384 monthly observations. The prices of commodities under study in this paper have been obtained from the International Monetary Fund (IMF) databank - http://www.imf.org/external/data.htm  Crude Oil (petroleum).  Data description: Price index, 2005 = 100, simple average of three spot prices; Dated Brent, West Texas Intermediate, and the Dubai Fateh.  Unit: US Dollars per barrel (US$/bbl.).  Maize (Corn).  Data description: U.S. No.2 Yellow, FOB Gulf of Mexico, U.S. price.  Unit: US Dollars per Metric Tonne (US$/mt).  Rice.  Description: 5% broken milled white rice, Thailand nominal price quote.  Unit: US Dollars per Metric Tonne (US$/mt).  Soybeans.  Description: Chicago Soybean futures contract, No. 2 yellow and par.  Unit: US Dollars per Metric Tonne (US$/mt).  Wheat.  Description: No.1 Hard Red Winter, ordinary protein, FOB Gulf of Mexico.  Unit: US Dollars per Metric Tonne (US$/mt). In the figure above, y axis is US Dollars per Metric tonne and x axis is year. Source: IMF 0 200 400 600 800 1,000 1,200 80 82 84 86 88 90 92 94 96 98 00 02 04 06 08 10 Crude Oil (petroleum) Maize (corn) RICE SOYBEANS WHEAT
  15. 15. 14 All the prices of the commodities are in their nominal rates. The length of the period is long enough to determine the long-run relationship between series if there exist any. However within this period, it has come to our notice that the prices of commodities have experienced higher rise especially over the last few years. The International Monetary Fund (2008) published figures that between January 2000 and March 2008, the price index for all primary commodities increased 204%. A prime contributor of this increase is the steep rise of 272% in petroleum prices and 107% in food prices. We know that there has been a global boom in commodity markets since the early 2000s driven by strong economic growth worldwide, but particularly in Asia. The rapid growth of emerging economies like China and India are having a big influence in the dynamics of the commodity markets. For example, the surge in oil price since 2003 is largely because of the growing demand for energy in China and India. Other significant changes have taken place over the course of the period such as the increased production of biofuel and the commercialization of biodiesel worldwide. The increase in biofuels production (especially in the United States, European Union) has not only increased demand for food commodities but also brought about shifts in land use to energy crops. There is also the food price crisis of 2007-08 which brought about the enormous price rise in food commodities due to the combination of various factors, with the rise in Oil Prices being one of the big factors. Baffes (2007) estimates that grain prices increase 0.18 percent for every one percent increase in the price of oil. If we study the figure, we can see that there’s an increase in the price of crude oil during 1990, which was primarily because of the increase in precautionary demand for oil as a result of the Gulf War. (Kilian, 2009). The nominal prices of crude oil remained below $40 /bbl until 2003, but have been on an upward trend since, and the cause for this price shock is believed to be because of the increasing demand for oil from the emerging economies like China and India. (Kilian, 2009; Hamilton, 2009). We can see the huge spikes in prices of all commodities during 2008. Agricultural commodity prices have been rising since 2002 and increasing sharply from 2007.The rise in food commodity prices was led by cereals, where from January 2005 until June 2008, maize prices almost tripled, wheat prices increased 127 percent and rice prices increased 170 percent (Mitchell 2008). The one that catches the eye is the large rise in rice prices. Rice prices almost tripled from January to April 2008 despite little change in production or stocks (Mitchell 2008). The swift increase was mainly a reaction to the rise in wheat prices in 2007 (up 88 percent from January to December) which raised concerns about low global grain supplies and encouraged several countries to ban rice exports to protect consumers from international price increases. The impact of these bans or restrictions is exemplified by how Thailand’s rice export price skyrocketed after India banned rice exports in October 2007. So we see the interdependence between sectors and how one causes a reaction in others.
  16. 16. 15 5. METHODOLOGY In this paper we will use a simple model to estimate the relationship between petroleum prices and prices of the following main food commodities- barley, maize, rice, soybean and wheat. We will test the hypothesis of whether the changes in petroleum prices play a significant role in changing the food commodity prices. The estimation is based on the following equation 1.1 (1.1) where is the price of food commodity (i) at time (t); is the price of petroleum at time (t) and is the error term. All variables are in logarithms. The model is estimated in logarithms in order to facilitate interpreting the estimated parameters as elasticities. To examine whether or not a stable linear steady-state relationship exist between the variables, we will need to carry out Unit root and Co-integration test. 5.1 UNIT ROOT TEST The Unit root test is used to determine the stationarity properties of the series. The presence of unit root proves that a series is non-stationary. A series is said to be non-stationary if the mean, variance and auto-covariance change over time (Hatanaka. M, 2003). However, a stationary series has a mean around which fluctuations revert (constant mean); a variation that is constant over time (constant variance); and auto-covariance that depend only on the distance apart in time (constant covariance). The need to test for the presence of unit root is to avoid the problem of spurious regression. Now in economic time series, it is commonly characterized by strong ‘trend-like behaviour’ and therefore the above conditions of stationarity are violated. So if this trend-like behaviour is not considered then the OLS estimators can give rise to misleading results and we can falsely imply that a meaningful economic relationship exist. This phenomenon is what was described by Granger and Newbold (1974) as spurious regression. There are ways of testing the presence of unit root or non-stationarity. A formal and commonly used test of non-stationarity is the Augmented Dickey-Fuller (ADF) test. We form the ADF regression, equation 1.2 ∑ where is the series under examination, is the constant, is the coefficient in the time trend series, is the lag order of the autoregressive process, and are lagged values of order one of and finally is the error term.
  17. 17. 16 The ADF test can be tested on at least three possible models: i) A pure random walk without a drift. It is defined by using the constraint in the above equation 1.2 and this leads to the following equation: ii) A random walk with a drift. It is obtained by using the constraint in equation 1.2 and leads to the following equation: iii) A deterministic trend with a drift. and equation 1.2 becomes The sign of the drift parameter ( ) causes the series to wander upward if positive and downward if negative, whereas the size of the absolute value affects the steepness of the series (Pfaff, 2006). The test procedure for unit roots is that, we have to test the Null if = 0, using t statistic critical values. So if = 0, it implies that the series contains a unit root. The most important point of focus is whether is statistically significant and for this we have to check the t ratio of the coefficient of the lagged level term . This t ratio is called the ADF statistic. At first we will test each of the series in their log levels. Being time series data and having trend-like behaviour, it is expected that they will be non-stationary and integrated of order one I(1) process. Next, we will test each of the series in their first difference. Since differencing induces stationarity, the first difference of each of the series will make it stationary and integrated of order zero I(0). If this is the case then the series is said to be integrated of order one I(1). Next step in this methodology is to test the existence (or absence) of co-integration between the variables. According to Engle and Granger (1987), two series integrated of the same order I(q) are said to be co-integrated, if the linear combination of the two variables generate a stationary series. A non-stationary series that is co-integrated may diverge in the short run but must be linked together in the long-run. The cointegrated variables will never move far apart, and will be attracted to their long- run relationship. Testing for cointegration implies testing for the existence of such a long-run relationship between economic variables.
  18. 18. 17 5.2 CO-INTEGRATING TEST The two most commonly used approaches to find long-run relationship between variables are the Engle Granger approach and the Johansen and Jesulius cointegration approach. In this study, since we are going to carry out the tests separately for each of the food commodities and try to find if there exists a long term relationship with crude oil prices. Therefore it being a bivariate approach, we are going to use the two step estimation procedure developed by Engle and Granger in 1987. According to this technique, to determine whether two variables are co-integrated, we first have to ascertain the order of integration of the variables that are being modeled. This pre-testing is done by the Unit root test as discussed previously. For co-integration to exist, two variables have to be integrated of the same order. If we establish that two variables are integrated of the same order, then we proceed next to estimating the long-run equilibrium relationship in the form of OLS regression line, such as (1.3) where is the y-intercept, is the slope and is the error term. Next, the estimated regression line is given the form: ̂ ̂ ̂ where ̂ ̅ ̂ ̅ and ̂ ∑ ̅ ̅ ∑ ̅ In order to determine if variables are cointegrated, we will have to test for unit roots in the residual sequence in equation 1.3 using ADF test. The residual sequence denoted by is a series of estimated values of the deviation from the long-run relationship and it is estimated as, ̂ We test for unit roots on residuals so as to determine if the deviations are stationary or not. If they are stationary, then the series co-integrate. The ADF test is carried out on the following model, ̂ ̂ (1.4) where ̂ are the estimated first differenced residuals, ̂ are the estimated lagged residuals, is the parameter of interest representing the slope of the line and are errors obtained in fitting both differenced residuals.
  19. 19. 18 Now to test the hypothesis on to determine whether the residuals are stationary, we will follow: Firstly, we set the Null and Alternative hypothesis as- Next, we determine the test statistic- ̂ ̂ ̂ where the value of ̂ is the standard error of ̂ , the estimate of Then we compare the test statistic obtained above with the critical values from the Dickey-Fuller table. If ̂ is greater than the critical value, we do not reject the null hypothesis The rejection of the Null hypothesis would mean that the residuals are stationary, which implies that the variables under study are co-integrated. This is the methodology to test for cointegration. The next step of the testing is to estimate the Error Correction Model (ECM) 5.3 ERROR CORRECTION MODEL (ECM) On finding cointegrating relationship, it only considers the long-run property of the model and does not deal with the short-run dynamics explicitly. A good time-series model must describe both the long-run and short-run effects of individual variables. For this purpose, we move on to the next step of our investigation, which is to estimate the Error Correction Model. They are a category of multiple time series models that directly estimate the speed at which a dependent variable-Y, returns to equilibrium after a change in an independent variable- X. It is defined as a dynamic model in which the movement of the variable in any period is related to the previous period’s gap from the long run equilibrium. Granger’s ‘Representation Theorem’ states that for every cointegrated relationship, there must exist a mechanism by which the equilibrium is maintained. Even when there exist a long run relationship, there will be deviations from the equilibrium and the correction or the adjustment process is described by what has become known as an Error Correction Model.
  20. 20. 19 A simple dynamic model of a short-run adjustment model is given by: (1.5) where is the dependent variable, is the independent variable, and are the lagged values of and ; are the parameters, and is the error term assumed to be One important point to put across at this point is that the problem associated with the short-run adjustment model is that of spurious correlation. This is the situation where two variables have no causal relation, yet they may be inferred that they do. This problem is solved by de-trending the data. Hence, we will estimate the first difference of equation 1.5 (1.6) Application of first differences removes the stochastic trend from variables and while de-trending is the step in the right direction, in that it removes the spurious regression problem of trends, but it also throws away valuable information about the long run behavior of the variables. So the solution to find the right balance is to adopt the Error Correction model which is as follows: And subtracting the term on both sides lead to (1.7) Next, we will subtract the term on both sides of equation 1.7 and we get: (1.8) Now we will rearrange equation 1.8 and we will get: [ ] (1.9) where and . So equation 1.9 is the Error correction Model (ECM). The economic interpretation of the following equation would go as; the immediate (or short-run impact) of on is given by , the long-run impact is given by , and the rate of adjustment to equilibrium is given by . Specifically, the ECM says that the current change in is proportional to the current change in and a correction to take account of the extent to which deviated from its equilibrium value corresponding to as given by [ ]. The negative sign attached to ensures that any disequilibria will be corrected. If tending to -1, then a large percentage of disequilibria is corrected from each period; if tending to 0, then the adjustment will be slow and if the sign is positive then it would imply that the system diverges from the long-run equilibrium path.
  21. 21. 20 Next, we will carry out a few diagnostic tests on the model obtained in order to determine if it satisfies a few assumptions. It is essential that the assumptions are satisfied to validate the results of the analysis. These assumptions are-  It is a Linear Regression model. The relationship between the explanatory variables and the outcome variable is linear. In other words, each increase by one unit in an explanatory variable is associated with a fixed increase in the outcome variable.  The residuals are normally distributed. This assumption is required in order to conduct hypothesis testing, particularly if the sample size is small. For sample sizes that are sufficiently large, violation of the normality assumption is virtually inconsequential.  The errors are statistically independent of each other. i.e. there is no serial correlation among residuals.  The variance of the residuals is constant. If this is the case, we call it Homoscedasticity, which is desirable. Therefore, we will have to carry out diagnostic tests to determine if any of the above assumptions have been violated. 5.4 DIAGNOSTIC TESTS To check the validity of the above assumptions, we will carry out the following tests:  The Jarque-Bera Normality test to check if the residuals are normally distributed.  The Breusch-Godfrey serial correlation LM test to detect the existence of serial correlation in the model.  The Breusch-Pagan-Godfrey test to detect heteroscedasticity.
  22. 22. 21 a) NORMALITY TEST We will use the Jarque-Bera normality test is used to determine whether the residuals in the Error Correction Model are normally distributed. This test measures the difference in kurtosis and skewness of a variable compared to those of the normal distribution (Jarque and Bera, 1980). In the Jarque-Bera test, the test statistic is: [ ] where is the number of observations, is the number of estimated parameters, is the skewness of the variable and is the kurtosis of the variable. The Null and Alternative hypothesis is set as follows: the residuals are normally distributed. the residuals are not normally distributed. We will reject the null if the p-value of the Jarque-Bera statistic is less than 5 percent (p ≤ 0.05). We want the p-value to be greater than 5 percent, so that it satisfies the assumption of the residuals being normally distributed. b) SERIAL CORRELATION TEST We will use the Breusch-Godfrey Serial Correlation LM test to check if residuals are serially correlated. If the errors are not uncorrelated, it would be stated that they are serially correlated and this is not desirable. This problem of autocorrelation is typically associated with time-series data. Serial correlation occurs in time-series studies when the errors associated with a given time period carry over into future time periods. For example, if we are predicting the growth of stock dividends, an overestimate in one year is likely to lead to overestimates in succeeding years. Now a formal way to test for autocorrelation is the Breusch-Godfrey test. The test statistic is given by: and the Hypothesis is given by: no serial correlation in the residuals. there is serial correlation in the residuals. We will reject the null if the p-value of the Obs* R-squared is less than 5 percent (p ≤ 0.05). We want the p-value to be greater than 5 percent, so that it satisfies the assumption of residuals not being serially correlated.
  23. 23. 22 c) HETEROSCEDATICITY TEST Heteroscedasticity results from a sequence of random variables having differing variances, i.e. variances of the residuals are not consistent. A formal way of testing this is by using the Breusch- Pagan-Godfrey test. The LM statistic is given by: and under Null hypothesis, this LM test has distribution. The Hypothesis is given by: residuals have constant variance (i.e. Homoscedastic) residuals are heteroscedastic. We will reject the null if the p-value of the Obs* R-squared is less than 5 percent (p ≤ 0.05). We want the p-value to be greater than 5 percent, so that it satisfies the assumption of homoscedasticity, which is desirable. I would also like to point out that there are a few shortcomings in this test. Firstly, we must specify a model of what we believe is the structure of the heteroscedasticity, if it exists. For example, the Breusch-Pagan test assumes that the error variance is a linear function of one or more of the explanatory variables, if heteroscedasticity exists. Thus, if heteroscedasticity exists, the error variance is a non-linear function of one or more explanatory variables and then this test will not be valid. Secondly, if the errors are not normally distributed, then these tests may not be valid. 5.5 CAUSALITY TEST We first tried to find long-term relationship between variables. Then we proceeded to find the short- term relationship or the adjustment process which enables the cointegrating relationship to maintain equilibrium. In this section, we will address the issue of the statistical concept of causality that is based on prediction. According to Granger causality, if a signal "Granger-causes" (or "G- causes") a signal , then past values of should contain information that helps predict above and beyond the information contained in past values of alone. Its mathematical formulation is based on linear regression modeling of stochastic processes (Granger 1969). The basic Granger causality definition is quite simple. If we have two terms and , and we attempt to forecast using past terms of Then is said to “Granger cause” if halps in the prediction of The definition leans on the idea that cause occurs before the effect and this is basis of most, if not all causality definitions. It also must be noted that we determine if there is two- way causation, i.e. if causes and if causes
  24. 24. 23 The Causality relationship can be evaluated by estimating the following linear regression models. For illustration, consider a bivariate linear autoregressive model of two variables and ∑ ∑ ∑ ∑ here is the number of lagged observations included in this model; the matrix A contains the coefficients of the model; and are residuals (prediction errors) for each time series. “If the variance of (or ) is reduced by the inclusion of the (or ) terms in the first (or second) equation, then it is said that (or ) Granger(G)- causes (or ). In other words, G- causes if the coefficients in are jointly significantly different from zero. This can be tested by performing an F-test of the null hypothesis that = 0, given assumptions of covariance stationarity on and . The magnitude of a G-causality interaction can be estimated by the logarithm of the corresponding F-statistic (Geweke, 1982). Note that model selection criteria, such as the Bayesian Information Criterion (BIC), (Schwarz 1978) or the Akaike Information Criterion (AIC), (Akaike 1974), can be used to determine the appropriate model order p.” (*) The Hypothesis is as following: doesn’t causes causes If the p-value is below 5 percent ((p ≤ 0.05), we will reject the null. This implies that there is causation. If the null cannot be rejected than it means that there is no causal relation between the variables. In other words, two variables are independent to each other. The important thing to point out here is that if the data of the variables have a trend, then it is most likely to show that there is correlation between them. However, we must note that in general, correlation doesn’t mean causation. So Granger Causality test is important as it highlights the presence of causation and it can be unidirectional or two way causation. (*) The above paragraph has been used to explain Granger Causality from the following piece: Anil Seth (2007), Scholarpedia, 2(7):1667
  25. 25. 24 6. RESULTS AND ANALYSIS The results of this paper are summarized in this section. This study used time series data for monthly prices of crude oil and the following food commodities- maize, rice, soybeans and wheat. The objective of the study is to find if there is a long term relationship between the crude oil prices and the food commodity prices between the period January 1980 to December 2011. To find the outcome, I carried out a series of tests, of which the methodology was discussed in the previous section. I will now present the results and discuss the findings. 6.1 AUGMENTED DICKEY-FULLER UNIT ROOT TEST We carry out this test as a standard pre-test to check for the existence of trend or in other words testing for the presence of unit roots. Although the presence of trend-like behavior is apparent in the time-series data and can be seen by simply plotting the data. However, choosing between the trend stationary and unit root process is difficult. Therefore, we will carry out the formal test of non- stationarity by using the ADF unit root test. The process of detecting the presence of unit roots is to check the absolute value of the ADF statistic obtained and if this value is greater than the 95% Critical value level, then we reject the null for the presence of unit root (i.e. non stationary series). Table 1 shows the results for the underlying price series in their levels and first differences. As we can see, the null hypothesis for the existence of unit root could not be rejected for each of the variables in their levels and therefore we can conclude that the series were non-stationary with presence of unit root at the 5% level of significance. Table 1. UNIT ROOT TEST Series Optimal Lag length (SC) ADF Statistic 95% Critical Values Inference lnp 1 -2.378347 -3.421631 I(1) dlnp 0 -14.11295* -2.868888 I(0) lnm 1 -2.482698 -3.421631 I(1) dlnm 0 -14.45643* -2.868888 I(0) lnr 2 -2.323841 -3.421662 I(1) dlnr 1 -12.73402* -2.868908 I(0) lns 1 -2.922845 -3.421631 I(1) dlns 0 -14.43345* -2.868888 I(0) lnw 1 -2.884889 -3.421631 I(1) dlnw 0 -14.97403* -2.868888 I(0) Notes: The Null Hypothesis : unit root exist (i.e. non-stationary series). The method to test this is to check the absolute value of the ADF Statistic and if it is greater than the 95% CV, then we can reject the Null. Hence, unit root doesn’t exist and the series is stationary I(0). * denotes significance at the 5% level.
  26. 26. 25 However, the null hypothesis was rejected for all the variables in their first differences, which implies that the series was made stationary by the application of first differences. So the series being non-stationary in the levels and on first differencing induces stationarity, goes on to imply that the series is integrated of order one and is denoted by I(1). Pre-testing variables is done to determine the order of integration of each variable. By definition, for two series to be co-integrated, it is necessary that they are integrated of the same order, ideally I(1). We have succeeded in finding this and we will proceed to the next step, which is to carry out the cointegration tests and it will enable us to confirm the existence (or absence) of long-run relationship between the crude oil prices and the food commodity prices. 6.2 CO-INTEGRATION ANALYSIS. We have identified that the price series of all the commodities are integrated of the same order. So we will next proceed to the formal testing of long-run cointegration by performing the Engle Granger two step procedure. We will test the bivariate relationship between oil prices and the food commodity prices using equation 1.1 as discussed in the methodology section. In order to determine if the variables are co-integrated, we will have to test for unit roots in the residuals. And if they are stationary, then the series co-integrate. We begin by estimating equation 1.3 (from the methodology section) in levels by OLS form: Taking the example of wheat prices to analyse the results; is crude oil price (the independent variable) and is the wheat price (the dependent variable). We get the following long-run estimate with the standard errors in parentheses: * (0.058) (0.017) =0.521 = 0.197 DW=0.098 The interpretations of the above results go as following. is the intercept in the regression equation. The value is significant at the 5% significance level. = 3.909 and it is the base level of the prediction, meaning that if the independent variable (crude oil) is zero, then this is the value for the dependent variable (wheat price). is the slope of the relation between crude oil price and wheat prices. So if the price of crude oil increases by 1 percent, then there will be an increase in the price of wheat by 0.348 percent. * Appendix 2.1
  27. 27. 26 statistic measures the success of the regression in predicting the values of the dependent variable within the sample. So, in this equation, 52.1% of the fraction of variance is explained by the model. DW is the Durbin Watson statistic, which measures the serial correlation in the residuals. As we can recall, we discussed in the methodology section that it is very important that the residuals follow some assumptions for the validity of the regression model. In the above model, a DW statistic of 0.098 is a strong indicator of serial correlation (which is undesirable). On further carrying out the Residual Diagnostics, we see that the model rejects the null for Normal distribution, no serial correlation and homoscedasticity. Hence it invalidates the standard estimation and inference of the model. This maybe because we have used a static model and have simply ignored the dynamic effects. Static models are very useful but they often mis-specify what the driving factors are. So we introduce a Dynamic model (with lagged terms). An Autoregressive Distributed Lag (ADL) model of first order is called ADL(1) model. On introducing dynamic terms to our above static model, the ADL(1) model for wheat would look like: On running the equation, we get the following long run estimates: * (0.059) (0.035) (0.015) (0.035) = 0.961 = 0.056 DW= 1.455 As evident, on the introduction of dynamic terms, the model improved. As we can see, the statistic improved and is close to 1. The Durbin Watson statistic too has improved significantly and is closer to 2.0, which implies being consistent with no serial correlation. We can also try an ADL(2) model, which might lead to even a better representation. So the important question that arises here is, how many lags do we need to include in our model? The most commonly used method of testing for lag length is the Information criteria. There are three namely- Akaike Information criterion (AIC), Schwarz Criterion (SC) and Hannan-Quinn (HQC). We will be using the Schwarz criterion (SC), as this is the most consistent (i.e. the probability of selecting the true model approaches one as sample grows). We will select the model with the lowest value of SC. And once we get our model, we can find the statistics of the model. However, the main task at first is to find if there is a long-term relationship between the variables. Next, are the steps to estimate the cointegration regression and establish if there is cointegration between crude oil price and food commodity price. We select the method COINTREG for the estimation setting dialogue. In order to obtain the same results as our static model, we will further select ‘Dynamic OLS’ for method and ‘None’ for the lag & lead length under the Non-stationary Estimation setting. On obtaining the Cointegrating Regression, we next select the Engle-Granger Cointegration test. By this series of steps, the software (Eviews) estimates m+1 different models, and selects the model with the optimal lag length. The order of integration of the residuals is estimated by evaluating the null of non-stationarity for the * Appendix 2.2
  28. 28. 27 ADF regression discussed in the methodology section. The residual ADF statistic is called the Engle- Granger ‘tau’ statistic. We will have to check the probability values (MacKinnon (1996) p-values) to see if the test statistic is large enough to reject the null of no cointegration. It is very important to point out that the critical values of the ADF test on the residuals are different from the ones used for testing of unit root in the series. The results are reported in Table 2. The null hypothesis of no cointegration was rejected for Maize, Soybeans and Wheat. Therefore, a long-run relationship exists between crude oil prices and the prices of maize, soybeans and wheat at the 5% level of significance or better. The results are consistent with the findings of Arshad and Hameed (2009); Ghaith and Awad (2011). The findings go on to confirm the significant role crude oil prices have on the food commodity prices. Firstly, as a production input and secondly, the dynamic effect it has because of the increasing demand for biofuels. Table 2. CO-INTEGRATION TEST Commodity Engle-Granger Tau Statistic Probability (*) Result Maize & Crude oil -3.948992 0.0093 Reject Null. Rice & Crude oil -3.040903 0.1033 Unable to reject Null. Soybeans & Crude Oil -3.859794 0.0122 Reject Null. Wheat & Crude Oil -4.184045 0.0043 Reject Null. Notes: The Null Hypothesis is that there is no co-integration. The method to test this is to check the p-value of the Engle-Granger test statistic. If the p-value is less than 5 percent (p-value ≤ 0.05), we then reject the Null of no co-integration. So there will be cointegration between the variables. * MacKinnon (1996) p-values So cointegration among non-stationary prices of crude oil and the three food commodities means that a linear combination of them was stationary and therefore, the prices tended to move towards the equilibrium relationship in the long-run. However, despite the three commodities (maize, soybean and wheat) being cointegrated with crude oil prices, there is rice for which we didn’t find co- integration with crude oil prices as the p-value of the Engle-Granger Tau statistic is above 5% level of significance, and this is too weak to be able to reject the null of no co-integration. Having found co-integrating relationship between crude oil price & maize, soybeans and wheat, we will now estimate the models for each food commodity with the optimal number of lags based on the Schwarz criterion (SC). And following this, we can establish the statistics and inferences of the long- run relationship estimates.
  29. 29. 28 Note: Numbers in parentheses under the coefficients are standard errors & The test results are in Appendix 2.4 MAIZE ADL (1) MODEL FOR MAIZE LNM = 0.1103 + 0.0251*LNP + 0.9634*LNM(-1) - 0.0052*LNP(-1) (0.0514) (0.035) (0.013) (0.036) = 0.9634 = 0.0574 DW= 1.3949 The coefficient of LNP is 0.0251, which implies that- if there is a 1 percent increase in the price of crude oil, then there will be a 0.0251 percent increase in the prices of maize. However, I must point out that the coefficient estimate is not significant at 5% significance level. We have established that there is long term relationship between fuel and maize prices but the estimate of the long-run relationship is not significant, therefore we cannot say how much fuel prices affect maize prices. However, with rising fuel prices, there is increasing demand for biofuels. And maize is a key feed stock for ethanol production. The US ethanol industry is also primarily corn based and there have been many significant structural changes taking place in maize production such as- in 2007 the US diverted more than 30 per cent of its maize production from food use to ethanol production. So with these changes, one would expect maize prices to be affected by fuel prices. Studies by Arshad and Hameed (2009); Ghaith and Awad (2011) found maize prices to be significantly influenced by fuel prices. Thereby supporting the theory above. However, in another study on this topic by Campiche et al. (2007), they found maize prices to be strongly influenced by fuel prices, but only during 2006-07 period. They didn’t find any co-integration during 2003-05. So it might be the case that, with biofuels taking more prominence in the energy sector only recently, the effects of fuel prices will be more evident with time. Yu et al. (2006) too in their study didn’t find long term relationship between crude oil and vegetable oils. But the author insists that the possible influence of crude oil price on edible oils will grow if high oil prices continue and edible oils become an increasing source of biodiesel. Similarly, even in our study, there is the possibility that the effect of fuel prices on maize prices will be more prominent with a more recent data period. SOYBEAN ADL (1) MODEL FOR SOYBEAN LNS = 0.1538 + 0.0887*LNP + 0.9641*LNS(-1) - 0.0755*LNP(-1) (0.154) (0.088) (0.964) (-0.076) = 0.9574 = 0.0564 DW= 1.3905 The coefficient of LNP is 0.0887,which implies that if there is a 1 percent increase in the price of crude oil, then there will be a 0.0887 percent increase in the prices of soybeans. And the good thing here is that the coefficient estimates are significant at the 5% level of significance unlike maize. The residual diagnostics were carried out and the model satisfied the assumptions of residuals being normally distributed, no serial correlation and homoscedastic. The soybean results show that fuel price has a significant effect on soybean prices. Soybean too is a food crop
  30. 30. 29 which is used as a feedstock for biodiesel production. Therefore, another crop whose prices can be affected because of the various dynamic effects. Soybean is the primary feedstock for the US biodiesel industry and there is also huge demand for soybean in China mainly to have good stock of livestock feed. So the dual demand surges from biofuels and Chinese oilseed needs are having a remarkable impact on the amount of U.S. land required to meet those needs. This is resulting in acreage shifting WHEAT ADL (1) MODEL FOR WHEAT LNW = 0.1584 + 0.0562*LNP + 0.9569*LNW(-1) - 0.0380*LNP(-1) (0.158) (0.056) (0.957) (-0.038) = 0.961 = 0.056 DW= 1.455 The coefficient of LNP here is 0.0562, which implies that- if there is a 1 percent increase in the price of crude oil, then there will be a 0.0562 percent increase in the prices of wheat. The coefficient estimate is significant at the borderline 10% level of significance. Hence, we can say that there is a weak relationship between the variables. Wheat is a crop that is being affected by fuel prices because of either rising production costs or acreage shifting to energy crops as a result of increasing biofuel demand. 6.3 SHORT-RUN ANALYSIS: THE ERROR CORRECTION MODEL. According to the Representation Theorem of Engle and Granger (1987), an Error Correction Model (ECM) can be estimated for two cointegrating variables. We found that prices of maize, soybeans & wheat are co-integrated to crude oil prices. So we will proceed to setting up the ECM for the three commodities to establish their short-run relationship and the mechanism which helps maintain the long-run equilibrium. However, we didn’t find co-integration between rice and crude oil prices. So we cannot say anything about the long run relationship in this case. Nevertheless, we will proceed to find the short-run relationship between crude oil and rice prices by using a method where we don’t use the Error Correction Model (ECM) term and evaluate only the short-term behavior. Firstly, we will discuss the findings of the ECM. The results are presented in Table 3. But before analysing the estimated coefficients of the Error Correction Models, I would like to discuss the steps that we have to take before estimating our ECM. We selected the models with the optimal number of lags for each food commodity with the help of Schwarz criterion (SC) and made our inferences about the long run relationship estimates between crude oil and food commodity prices. Now using those
  31. 31. 30 models, we will estimate our ECM. The methodology for setting the up the model has been discussed in the methodology section. I will discuss one example with the help of an illustrated equation. The ECM of an ADL(1) for Soybean, with the standard error in parentheses; After putting the coefficient estimate values obtained, we get- (0.003) (0.035) (0.014) is the coefficient which will help us establish the short-run impact that the change in crude oil prices will have on soybean prices. The results indicate that if there is 1 percentage point increase in the rate of rise in crude oil prices, then the rate of increase in the soybean prices will be 0.0883 percent. The estimated coefficient is significant at the 5% significance level. is the other statistic of importance and it is the coefficient of Res(-1). Now Res(-1) is the one lagged difference of the residuals we obtained from the static regression equation of soybean and crude oil prices. We must also note that if the sign of the coefficient is negative, it is implying the deviations from the equilibrium that are corrected. The magnitude of the error correction term here indicates that around 0.0358 percent of the disequilibrium is corrected monthly to maintain the long- run equilibrium. The coefficient is significant at the 5% significance level. We also have carry out the residual diagnostics to ensure that the errors of the ECM satisfy the usual assumptions. The null for residuals being normally distributed couldn’t be rejected as the p-value of the Jarque Bera statistic was 0.08612, which is greater than 0.05. The Null for homoscedasticity too couldn’t be rejected as the p-value (chi-square) for the observed R-squared value was 0.1028, which is again greater than 0.05, so we therefore cannot reject the null. Finally the test for serial correlation, the p-value of the observed R-squared was 0.3185, which is greater than 0.05. And therefore we cannot reject null of no serial correlation. Table 3. ERROR CORRECTION MODEL Dependent variable Independent variable (crude oil) d(lnp) Coefficient ECT Maize d(lnm) 0.023756 (0.5043) -0.036757* (0.0061) Soybeans d(lns) 0.088304* (0.0118) -0.035825* (0.0099) Wheat d(lnw) 0.055609** (0.1090) -0.043033* (0.0033) Notes: numbers in parentheses are the p-values (MacKinnon (1996) p-values). * significance at 5% level of significance or better. ** significance at 10% level of significance.
  32. 32. 31 Table 3 summarizes the coefficient estimates obtained from the Error Correction Models. Firstly, we can see that the sign of the coefficients of the error correction terms are negative and therefore implying that the deviations from the equilibrium are corrected. The coefficient estimates are all significant at 1% level of significance. And in the second column, we see that 0.036% for maize and 0.043% of the disequilibrium is corrected every month for wheat to help maintain the long-run relationship between the following food commodities and the crude oil prices. We also see that if there is a 1 percentage point increase in the rate of rise in crude oil prices, then the rate of increase in the maize prices will be 0.0237 percent and the rate of increase in the wheat prices will be 0.0556 percent. However, among the two, the coefficient estimate of maize prices is insignificant and wheat prices are only significant at borderline 10% level of significance. Finally, since we didn’t find cointegrating relationship between crude oil price and price of rice, we didn’t estimate the ECM. But we did estimate a short-run model for Rice without using the error correction term. The results were inferring that if there is a 1 percentage point increase in the rate of rise in crude oil prices, then the short-run impact on rice prices will be that the rate of increase will be 0.0185 percent. But the coefficient estimate results were insignificant. 6.4 CAUSALITY TESTS In this section, we discuss the results of the Granger Causality test summarized in Table 4. We find from our tests that there is significant causal relationship from crude oil prices to each of the food commodity prices used in our study. The results show that crude oil prices ‘Granger cause’ the prices of maize, rice, soybean, wheat and the findings are significant at the 5% level of significance. However, there is causation in only one direction and the results do not indicate reverse causation of food commodity prices too having a causal effect on crude oil prices. So the test highlights the presence of only unidirectional causality. This outcome was expected in the sense, from our previous discussions about the effects of oil prices on food commodity prices. With increase in oil prices, there was the supply side effect which caused agricultural production cost to rise and thereby affecting grain prices. There is also the demand side effect as food commodities compete with derived demand for biofuels. So as we can see, there are various linkages through which oil prices can affect food price and our results validate these points. Our results are also consistent with the findings Arshad and Hameed (2009) who too found unidirectional long-run causality flowing from petroleum prices to cereal prices.
  33. 33. 32 Table 4. GRANGER CAUSALITY TEST Commodity Hypothesis F- Statistics p-value Causal Reference Crude oil (lnp) & Maize (lnm) LNP does not Granger Cause LNM LNM does not Granger Cause LNP 6.24676 0.73809 0.0021 0.4787 lnp lnm Crude oil (lnp) & Rice (lnr) LNP does not Granger Cause LNR LNR does not Granger Cause LNP 4.28279 0.57702 0.0145 0.5621 lnp lnr Crude oil (lnp) & Soybeans (lns) LNP does not Granger Cause LNS LNS does not Granger Cause LNP 3.45528 0.90996 0.0326 0.4034 lnp lns Crude oil (lnp) & Wheat (lnw) LNP does not Granger Cause LNW LNW does not Granger Cause LNP 4.39446 1.23447 0.0130 0.2922 lnp lnw Notes: The Null Hypothesis as mentioned above is for causation (Granger cause) not taking place. If the p-value is lesser than 5 percent (p-value ≤ 0.05), we then reject the Null and it therefore implies that a particular causation does take place.
  34. 34. 33 7. CONCLUSION The motivation to work on this topic was mainly to learn about the nature of the rise in prices of agricultural food commodities in the year 2008 and the factors that contributed to this price rise. It is understood that oil price is one of the factors as it is an agriculture production input. For instance, the prices of fertilizer, fuel, and transportation were found to be affected by the crude oil price directly and subsequently influenced the production of grain commodities. However, there is another dimension as to how oil prices are now affecting food prices and that is with the increasing demand for biofuels. So it is primarily because of the above two dynamics that I wanted to investigate if there is a long term relationship between crude oil prices and food commodity prices. This is an important issue in present times, with the high prices and price volatility in the oil and food commodity markets. However, this topic is relatively new and discussions have started mainly post the 2008 food price crisis. I tried to examine if there exist a cointegrating relationship between the two prices and I used the data for the period between 1980 to 2011. The food commodities that I selected were maize, rice, soybean and wheat. I carried out the Engle-Granger Co-integration test and found maize, soybean and wheat to be cointegrated with crude oil prices. But, rice prices were not found to be cointegrated. I also carried out the Granger Causality test and the results exhibited unidirectional causality, with only crude oil prices ‘Granger causing’ each of the four food commodity prices. The reverse was not true, as crude oil prices were not found to be influenced by price of food commodities. So from our results we can confirm the significance of oil prices and the impact it has on the food commodity prices. In this study, I also found the short run relationship between oil and food prices. The short-run impact of fuel prices on food prices was found to be small and it was significant only for soybean and wheat. The results for maize were insignificant in the short-run and long-run. Now maize is a very important crop which not only has food use but other non-food use such as feed grain for livestock, ethanol production etc. With rise in fuel prices, it is expected to have an impact on maize prices. Firstly, with increasing demand for biofuels- more share of maize production is being diverted towards ethanol production and there is also the shifting acreage away from other crops such as wheat to maize. Therefore, these structural changes are supposed to have dynamic effects leading to changes in maize prices. Hence, despite these findings, I am convinced that there is strong relationship between fuel and maize prices. I must also point out that this study has many limitations. Firstly, I have adopted a very simple bivariate model. To obtain results that can capture the dynamic effects of how changes in fuel prices affect food prices, we would require to have more variables that can explain the model better. I also didn’t take any structural breaks in the data. The time span of the data is a very important factor in obtaining accurate results. Lastly, I only tried to study the effect oil prices have on food commodity prices and to test the direction of causality. But the study would have been richer if I could have captured the effect one food commodity is having on another food commodity. Nevertheless, despite the above setbacks, I can confirm from this study that there exist a long run relationship between fuel and food commodity prices and that this role is only going to become even more significant with the development and expansion of the biofuel industry.
  35. 35. 34 BIBLIOGRAPHY Yu, Tun-Hsiang, D.A. Bessler, and S. Fuller. (2006). “Cointegration and Causality Analysis of World Vegetable Oil and Crude Oil Prices.” Selected Paper prepared for presentation at the American Agricultural Economics Association Annual Meeting, Long Beach, CA July 23-26. In, F. and B. Inder. (1997). “Long-run Relationships between World Vegetable Oil Prices.” Australian Journal of Agricultural and Resources Economics 41: 455-70. Abbott, P., Hurt, C., and Tyner, W. (2008). What's Driving Food Prices? Farm Foundation Issue Report. Illinois, USA: Farm Foundation, pp. 23-34. Abdel Hameed, A. A., and Arshad, F. M. (2008). The Impact of Petroleum Prices on Vegetable Oils Prices: Evidence from Co-integration Tests. Paper presented at the International Borneo Business Conference on Global Changes, Malaysia, 15-17 December, 2008. Campiche, J., Bryant, H., Richardson, J., and Outlaw, J. (2007). Examining the Evolving Correspondence between Petroleum Prices and Agricultural Commodity Prices. Paper presented at the American Agricultural Economics Association Annual Meeting, Portland, OR, July 29-August 1, 2007. Arshad, F. M., and Abdel Hameed, A. A. (2009). The Long Run Relationship Between Petroleum and Cereal Prices, Global Economy and Finance Journal, Vol.2, No.2, pp. 91-100. Engle, R. F., and Granger, C. W. J. (1987). Co-Integration and Error-Correction: Representation, Estimation, and Testing. Econometrica. Vol.55, pp. 251-276. Von Braun, J., et al. (2008). High Food Prices: The What, Who, and How of Proposed Policy Actions. Washington, DC, USA: International Food Policy Research Institute, pp. 3-10. Baffes, J. and T. Haniotis (2010). "Placing the 2006/08 Commodity Price Boom into Perspective" World Bank Policy Research Working Paper, No. 5371. Esmaeili, A. and Shokoohi, Z, (2011). "Assessing the effects of oil price on world food prices: application of principal-component analysis" Energy Policy, 39: 1022-1025. FAO (2003). "Market Integration and Price Transmission in Selected Food and Cash Crop Markets of Developing Countries: Review and Applications", by Rapsomanikis, G., Hallam, D., and P. Conforti, in Commodity Market Review 2003-2004., Commodities and Trade Division, FAO, Rome. Trostle, R. (2008). "Global Agricultural Supply and Demand: Factors Contributing to the Recent Increase in Food Commodity Prices"; A Report from the Economic Research Service, United States Department of Agriculture, WRS-0801, July.
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  37. 37. 36 APPENDIX UNIT ROOT TEST 1) lnp Null Hypothesis: LNP has a unit root Exogenous: Constant, Linear Trend Lag Length: 1 (Automatic - based on SIC, maxlag=16) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -2.378347 0.3903 Test critical values: 1% level -3.982264 5% level -3.421631 10% level -3.133608 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LNP) Method: Least Squares Date: 09/12/12 Time: 19:13 Sample (adjusted): 1980M03 2011M12 Included observations: 382 after adjustments Variable Coefficient Std. Error t-Statistic Prob. LNP(-1) -0.019896 0.008366 -2.378347 0.0179 D(LNP(-1)) 0.317064 0.048754 6.503318 0.0000 C 0.048889 0.024535 1.992638 0.0470 @TREND(1980M01) 0.000102 4.43E-05 2.307206 0.0216 R-squared 0.113946 Mean dependent var 0.002851 Adjusted R-squared 0.106913 S.D. dependent var 0.082915 S.E. of regression 0.078357 Akaike info criterion -2.244664 Sum squared resid 2.320858 Schwarz criterion -2.203351 Log likelihood 432.7308 Hannan-Quinn criter. -2.228274 F-statistic 16.20345 Durbin-Watson stat 1.975446 Prob(F-statistic) 0.000000
  38. 38. 37 2) d(lnp) Null Hypothesis: D(LNP) has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=16) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -14.11295 0.0000 Test critical values: 1% level -3.447259 5% level -2.868888 10% level -2.570751 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LNP,2) Method: Least Squares Date: 09/12/12 Time: 19:15 Sample (adjusted): 1980M03 2011M12 Included observations: 382 after adjustments Variable Coefficient Std. Error t-Statistic Prob. D(LNP(-1)) -0.687759 0.048732 -14.11295 0.0000 C 0.001965 0.004038 0.486581 0.6268 R-squared 0.343895 Mean dependent var 1.32E-05 Adjusted R-squared 0.342168 S.D. dependent var 0.097245 S.E. of regression 0.078873 Akaike info criterion -2.236746 Sum squared resid 2.363933 Schwarz criterion -2.216089 Log likelihood 429.2184 Hannan-Quinn criter. -2.228551 F-statistic 199.1753 Durbin-Watson stat 1.969711 Prob(F-statistic) 0.000000
  39. 39. 38 3) lnm Null Hypothesis: LNM has a unit root Exogenous: Constant, Linear Trend Lag Length: 1 (Automatic - based on SIC, maxlag=16) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -2.482698 0.3366 Test critical values: 1% level -3.982264 5% level -3.421631 10% level -3.133608 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LNM) Method: Least Squares Date: 09/12/12 Time: 19:16 Sample (adjusted): 1980M03 2011M12 Included observations: 382 after adjustments Variable Coefficient Std. Error t-Statistic Prob. LNM(-1) -0.025801 0.010392 -2.482698 0.0135 D(LNM(-1)) 0.305873 0.049280 6.206819 0.0000 C 0.115456 0.047953 2.407686 0.0165 @TREND(1980M01) 4.76E-05 2.77E-05 1.722465 0.0858 R-squared 0.101271 Mean dependent var 0.002139 Adjusted R-squared 0.094138 S.D. dependent var 0.057897 S.E. of regression 0.055104 Akaike info criterion -2.948772 Sum squared resid 1.147780 Schwarz criterion -2.907458 Log likelihood 567.2154 Hannan-Quinn criter. -2.932382 F-statistic 14.19801 Durbin-Watson stat 2.012528 Prob(F-statistic) 0.000000
  40. 40. 39 4) d(lnm) Null Hypothesis: D(LNM) has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=16) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -14.45643 0.0000 Test critical values: 1% level -3.447259 5% level -2.868888 10% level -2.570751 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LNM,2) Method: Least Squares Date: 09/12/12 Time: 19:17 Sample (adjusted): 1980M03 2011M12 Included observations: 382 after adjustments Variable Coefficient Std. Error t-Statistic Prob. D(LNM(-1)) -0.708844 0.049033 -14.45643 0.0000 C 0.001411 0.002840 0.496701 0.6197 R-squared 0.354826 Mean dependent var -0.000362 Adjusted R-squared 0.353128 S.D. dependent var 0.068952 S.E. of regression 0.055457 Akaike info criterion -2.941201 Sum squared resid 1.168676 Schwarz criterion -2.920544 Log likelihood 563.7693 Hannan-Quinn criter. -2.933006 F-statistic 208.9883 Durbin-Watson stat 1.997449 Prob(F-statistic) 0.000000
  41. 41. 40 5) lnr Null Hypothesis: LNR has a unit root Exogenous: Constant, Linear Trend Lag Length: 2 (Automatic - based on SIC, maxlag=16) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -2.323841 0.4195 Test critical values: 1% level -3.982328 5% level -3.421662 10% level -3.133626 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LNR) Method: Least Squares Date: 09/12/12 Time: 19:18 Sample (adjusted): 1980M04 2011M12 Included observations: 381 after adjustments Variable Coefficient Std. Error t-Statistic Prob. LNR(-1) -0.020436 0.008794 -2.323841 0.0207 D(LNR(-1)) 0.425151 0.050666 8.391167 0.0000 D(LNR(-2)) -0.137866 0.051127 -2.696541 0.0073 C 0.107488 0.048918 2.197314 0.0286 @TREND(1980M01) 4.78E-05 2.75E-05 1.740656 0.0826 R-squared 0.169817 Mean dependent var 0.000883 Adjusted R-squared 0.160985 S.D. dependent var 0.061806 S.E. of regression 0.056613 Akaike info criterion -2.892124 Sum squared resid 1.205087 Schwarz criterion -2.840381 Log likelihood 555.9496 Hannan-Quinn criter. -2.871594 F-statistic 19.22799 Durbin-Watson stat 1.995732 Prob(F-statistic) 0.000000
  42. 42. 41 6) d(lnr) Null Hypothesis: D(LNR) has a unit root Exogenous: Constant Lag Length: 1 (Automatic - based on SIC, maxlag=16) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -12.73402 0.0000 Test critical values: 1% level -3.447304 5% level -2.868908 10% level -2.570761 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LNR,2) Method: Least Squares Date: 09/12/12 Time: 19:18 Sample (adjusted): 1980M04 2011M12 Included observations: 381 after adjustments Variable Coefficient Std. Error t-Statistic Prob. D(LNR(-1)) -0.728201 0.057185 -12.73402 0.0000 D(LNR(-1),2) 0.151606 0.050871 2.980172 0.0031 C 0.000580 0.002919 0.198819 0.8425 R-squared 0.331757 Mean dependent var -0.000228 Adjusted R-squared 0.328221 S.D. dependent var 0.069505 S.E. of regression 0.056968 Akaike info criterion -2.884810 Sum squared resid 1.226745 Schwarz criterion -2.853764 Log likelihood 552.5563 Hannan-Quinn criter. -2.872492 F-statistic 93.83129 Durbin-Watson stat 1.997295 Prob(F-statistic) 0.000000
  43. 43. 42 7) lns Null Hypothesis: LNS has a unit root Exogenous: Constant, Linear Trend Lag Length: 1 (Automatic - based on SIC, maxlag=16) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -2.922845 0.1564 Test critical values: 1% level -3.982264 5% level -3.421631 10% level -3.133608 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LNS) Method: Least Squares Date: 09/12/12 Time: 19:19 Sample (adjusted): 1980M03 2011M12 Included observations: 382 after adjustments Variable Coefficient Std. Error t-Statistic Prob. LNS(-1) -0.032675 0.011179 -2.922845 0.0037 D(LNS(-1)) 0.308360 0.049068 6.284282 0.0000 C 0.171950 0.059746 2.878020 0.0042 @TREND(1980M01) 4.55E-05 2.73E-05 1.666655 0.0964 R-squared 0.106083 Mean dependent var 0.001450 Adjusted R-squared 0.098989 S.D. dependent var 0.057227 S.E. of regression 0.054321 Akaike info criterion -2.977409 Sum squared resid 1.115377 Schwarz criterion -2.936096 Log likelihood 572.6851 Hannan-Quinn criter. -2.961019 F-statistic 14.95275 Durbin-Watson stat 1.994878 Prob(F-statistic) 0.000000
  44. 44. 43 8) d(lns) Null Hypothesis: D(LNS) has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=16) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -14.43345 0.0000 Test critical values: 1% level -3.447259 5% level -2.868888 10% level -2.570751 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LNS,2) Method: Least Squares Date: 09/12/12 Time: 19:19 Sample (adjusted): 1980M03 2011M12 Included observations: 382 after adjustments Variable Coefficient Std. Error t-Statistic Prob. D(LNS(-1)) -0.708358 0.049078 -14.43345 0.0000 C 0.001003 0.002805 0.357675 0.7208 R-squared 0.354098 Mean dependent var -8.24E-05 Adjusted R-squared 0.352398 S.D. dependent var 0.068112 S.E. of regression 0.054812 Akaike info criterion -2.964599 Sum squared resid 1.141649 Schwarz criterion -2.943942 Log likelihood 568.2383 Hannan-Quinn criter. -2.956404 F-statistic 208.3244 Durbin-Watson stat 1.980909 Prob(F-statistic) 0.000000
  45. 45. 44 9) lnw Null Hypothesis: LNW has a unit root Exogenous: Constant, Linear Trend Lag Length: 1 (Automatic - based on SIC, maxlag=16) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -2.884889 0.1686 Test critical values: 1% level -3.982264 5% level -3.421631 10% level -3.133608 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LNW) Method: Least Squares Date: 09/12/12 Time: 19:20 Sample (adjusted): 1980M03 2011M12 Included observations: 382 after adjustments Variable Coefficient Std. Error t-Statistic Prob. LNW(-1) -0.031951 0.011075 -2.884889 0.0041 D(LNW(-1)) 0.271601 0.049562 5.479974 0.0000 C 0.152611 0.054067 2.822641 0.0050 @TREND(1980M01) 5.40E-05 2.82E-05 1.911438 0.0567 R-squared 0.087283 Mean dependent var 0.001160 Adjusted R-squared 0.080040 S.D. dependent var 0.056671 S.E. of regression 0.054355 Akaike info criterion -2.976128 Sum squared resid 1.116807 Schwarz criterion -2.934814 Log likelihood 572.4404 Hannan-Quinn criter. -2.959738 F-statistic 12.04944 Durbin-Watson stat 1.981606 Prob(F-statistic) 0.000000
  46. 46. 45 10) d(lnw) Null Hypothesis: D(LNW) has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=16) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -14.97403 0.0000 Test critical values: 1% level -3.447259 5% level -2.868888 10% level -2.570751 *MacKinnon (1996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(LNW,2) Method: Least Squares Date: 09/12/12 Time: 19:21 Sample (adjusted): 1980M03 2011M12 Included observations: 382 after adjustments Variable Coefficient Std. Error t-Statistic Prob. D(LNW(-1)) -0.742870 0.049611 -14.97403 0.0000 C 0.000844 0.002807 0.300733 0.7638 R-squared 0.371092 Mean dependent var -7.00E-05 Adjusted R-squared 0.369437 S.D. dependent var 0.069061 S.E. of regression 0.054840 Akaike info criterion -2.963575 Sum squared resid 1.142819 Schwarz criterion -2.942918 Log likelihood 568.0428 Hannan-Quinn criter. -2.955380 F-statistic 224.2216 Durbin-Watson stat 1.972185 Prob(F-statistic) 0.000000
  47. 47. 46 2. CO-INTEGRATION TEST (ENGLE-GRANGER TWO STEP METHOD) 2.1 STATIC REGRESSION EQUATION FOR WHEAT Dependent Variable: LNW Method: Least Squares Date: 09/18/12 Time: 22:58 Sample: 1980M01 2011M12 Included observations: 384 Variable Coefficient Std. Error t-Statistic Prob. LNP 0.348408 0.017083 20.39513 0.0000 C 3.909750 0.058119 67.27165 0.0000 R-squared 0.521280 Mean dependent var 5.077279 Adjusted R-squared 0.520027 S.D. dependent var 0.283913 S.E. of regression 0.196695 Akaike info criterion -0.409125 Sum squared resid 14.77924 Schwarz criterion -0.388549 Log likelihood 80.55208 Hannan-Quinn criter. -0.400964 F-statistic 415.9612 Durbin-Watson stat 0.098064 Prob(F-statistic) 0.000000 2.2 ADL(1) MODEL FOR WHEAT Dependent Variable: LNW Method: Least Squares Date: 09/19/12 Time: 00:07 Sample (adjusted): 1980M02 2011M12 Included observations: 383 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.158466 0.059408 2.667411 0.0080 LNP 0.056210 0.034651 1.622177 0.1056 LNW(-1) 0.956973 0.014585 65.61145 0.0000 LNP(-1) -0.038020 0.034995 -1.086444 0.2780 R-squared 0.961491 Mean dependent var 5.077041 Adjusted R-squared 0.961186 S.D. dependent var 0.284246 S.E. of regression 0.056000 Akaike info criterion -2.916538 Sum squared resid 1.188548 Schwarz criterion -2.875305 Log likelihood 562.5170 Hannan-Quinn criter. -2.900182
  48. 48. 47 F-statistic 3154.277 Durbin-Watson stat 1.455045 Prob(F-statistic) 0.000000 2.3 a) MAIZE Cointegration Test - Engle-Granger Date: 09/12/12 Time: 19:28 Equation: UNTITLED Specification: LNM LNP C Cointegrating equation deterministics: C Null hypothesis: Series are not cointegrated Automatic lag specification (lag=1 based on Schwarz Info Criterion, maxlag=16) Value Prob.* Engle-Granger tau-statistic -3.948992 0.0093 Engle-Granger z-statistic -32.44131 0.0034 *MacKinnon (1996) p-values. b) RICE Cointegration Test - Engle-Granger Date: 09/12/12 Time: 19:34 Equation: UNTITLED Specification: LNR LNP C Cointegrating equation deterministics: C Null hypothesis: Series are not cointegrated Automatic lag specification (lag=2 based on Schwarz Info Criterion, maxlag=16) Value Prob.* Engle-Granger tau-statistic -3.040903 0.1033 Engle-Granger z-statistic -18.88773 0.0668 *MacKinnon (1996) p-values. c) SOYBEANS Cointegration Test - Engle-Granger Date: 09/12/12 Time: 19:36 Equation: UNTITLED Specification: LNS LNP C Cointegrating equation deterministics: C Null hypothesis: Series are not cointegrated Automatic lag specification (lag=1 based on Schwarz Info Criterion, maxlag=16) Value Prob.* Engle-Granger tau-statistic -3.859794 0.0122
  49. 49. 48 Engle-Granger z-statistic -30.18080 0.0057 *MacKinnon (1996) p-values. d) WHEAT Cointegration Test - Engle-Granger Date: 09/12/12 Time: 19:39 Equation: UNTITLED Specification: LNW LNP C Cointegrating equation deterministics: C Null hypothesis: Series are not cointegrated Automatic lag specification (lag=1 based on Schwarz Info Criterion, maxlag=16) Value Prob.* Engle-Granger tau-statistic -4.184045 0.0043 Engle-Granger z-statistic -35.24678 0.0018 *MacKinnon (1996) p-values. 2.4 LONG-RUN RELATIONSHIP MODELS a) MAIZE ADL(1) Dependent Variable: LNM Method: Least Squares Date: 09/19/12 Time: 01:10 Sample (adjusted): 1980M02 2011M12 Included observations: 383 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.110362 0.051418 2.146362 0.0325 LNP 0.025146 0.035497 0.708409 0.4791 LNM(-1) 0.963403 0.013308 72.39142 0.0000 LNP(-1) -0.005216 0.035893 -0.145310 0.8845 R-squared 0.963421 Mean dependent var 4.779135 Adjusted R-squared 0.963131 S.D. dependent var 0.299021 S.E. of regression 0.057416 Akaike info criterion -2.866612 Sum squared resid 1.249394 Schwarz criterion -2.825379 Log likelihood 552.9561 Hannan-Quinn criter. -2.850255 F-statistic 3327.376 Durbin-Watson stat 1.394951 Prob(F-statistic) 0.000000
  50. 50. 49 b) SOYBEANS ADL(1) Dependent Variable: LNS Method: Least Squares Date: 09/19/12 Time: 01:29 Sample (adjusted): 1980M02 2011M12 Included observations: 383 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.153845 0.064584 2.382111 0.0177 LNP 0.088794 0.034923 2.542549 0.0114 LNS(-1) 0.964197 0.013826 69.73945 0.0000 LNP(-1) -0.075559 0.035178 -2.147924 0.0324 R-squared 0.957465 Mean dependent var 5.501739 Adjusted R-squared 0.957128 S.D. dependent var 0.272565 S.E. of regression 0.056436 Akaike info criterion -2.901027 Sum squared resid 1.207128 Schwarz criterion -2.859794 Log likelihood 559.5466 Hannan-Quinn criter. -2.884670 F-statistic 2843.743 Durbin-Watson stat 1.390485 Prob(F-statistic) 0.000000 c) WHEAT ADL(1) Dependent Variable: LNW Method: Least Squares Date: 09/19/12 Time: 01:33 Sample (adjusted): 1980M02 2011M12 Included observations: 383 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.158466 0.059408 2.667411 0.0080 LNP 0.056210 0.034651 1.622177 0.1056 LNW(-1) 0.956973 0.014585 65.61145 0.0000 LNP(-1) -0.038020 0.034995 -1.086444 0.2780 R-squared 0.961491 Mean dependent var 5.077041 Adjusted R-squared 0.961186 S.D. dependent var 0.284246 S.E. of regression 0.056000 Akaike info criterion -2.916538 Sum squared resid 1.188548 Schwarz criterion -2.875305 Log likelihood 562.5170 Hannan-Quinn criter. -2.900182 F-statistic 3154.277 Durbin-Watson stat 1.455045 Prob(F-statistic) 0.000000
  51. 51. 50 3. ERROR CORRECTION MODEL 1) MAIZE Dependent Variable: D(LNM) Method: Least Squares Date: 09/12/12 Time: 19:49 Sample (adjusted): 1980M02 2011M12 Included observations: 383 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.002240 0.002940 0.762020 0.4465 D(LNP) 0.023756 0.035540 0.668429 0.5043 RES1(-1) -0.036757 0.013329 -2.757733 0.0061 R-squared 0.020536 Mean dependent var 0.002339 Adjusted R-squared 0.015381 S.D. dependent var 0.057954 S.E. of regression 0.057506 Akaike info criterion -2.866050 Sum squared resid 1.256641 Schwarz criterion -2.835125 Log likelihood 551.8485 Hannan-Quinn criter. -2.853782 F-statistic 3.983663 Durbin-Watson stat 1.385456 Prob(F-statistic) 0.019400 2) SOYBEANS Dependent Variable: D(LNS) Method: Least Squares Date: 09/12/12 Time: 19:53 Sample (adjusted): 1980M02 2011M12 Included observations: 383 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.001213 0.002883 0.420761 0.6742 D(LNP) 0.088304 0.034878 2.531790 0.0118 RES3(-1) -0.035825 0.013813 -2.593626 0.0990 R-squared 0.031897 Mean dependent var 0.001475 Adjusted R-squared 0.026802 S.D. dependent var 0.057154 S.E. of regression 0.056383 Akaike info criterion -2.905505 Sum squared resid 1.208026 Schwarz criterion -2.874580 Log likelihood 559.4042 Hannan-Quinn criter. -2.893238 F-statistic 6.260196 Durbin-Watson stat 1.389001
  52. 52. 51 Prob(F-statistic) 0.002114 3) WHEAT Dependent Variable: D(LNW) Method: Least Squares Date: 09/12/12 Time: 19:54 Sample (adjusted): 1980M02 2011M12 Included observations: 383 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.000950 0.002861 0.332110 0.7400 D(LNP) 0.055609 0.034612 1.606613 0.1090 RES4(-1) -0.043033 0.014574 -2.952667 0.0033 R-squared 0.027816 Mean dependent var 0.001113 Adjusted R-squared 0.022699 S.D. dependent var 0.056604 S.E. of regression 0.055958 Akaike info criterion -2.920635 Sum squared resid 1.189886 Schwarz criterion -2.889710 Log likelihood 562.3016 Hannan-Quinn criter. -2.908367 F-statistic 5.436161 Durbin-Watson stat 1.453261 Prob(F-statistic) 0.004702 Short-run relationship for RICE (without ECM term) Dependent Variable: D(LNR) Method: Least Squares Date: 09/17/12 Time: 18:39 Sample (adjusted): 1980M03 2011M12 Included observations: 382 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 0.192670 0.053053 3.631615 0.0003 D(LNP) 0.018576 0.037397 0.496728 0.6197 LNP(-2) 0.025040 0.006637 3.772787 0.0002 LNR(-2) -0.048469 0.011111 -4.362478 0.0000 R-squared 0.053111 Mean dependent var 0.000983 Adjusted R-squared 0.045596 S.D. dependent var 0.061756 S.E. of regression 0.060332 Akaike info criterion -2.767500 Sum squared resid 1.375890 Schwarz criterion -2.726187 Log likelihood 532.5925 Hannan-Quinn criter. -2.751110 F-statistic 7.067383 Durbin-Watson stat 1.298190
  53. 53. 52 Prob(F-statistic) 0.000124 4. GRANGER CAUSALITY TEST 1) MAIZE Pairwise Granger Causality Tests Date: 09/12/12 Time: 19:56 Sample: 1980M01 2011M12 Lags: 2 Null Hypothesis: Obs F-Statistic Prob. LNP does not Granger Cause LNM 382 6.24676 0.0021 LNM does not Granger Cause LNP 0.73809 0.4787 2) RICE Pairwise Granger Causality Tests Date: 09/12/12 Time: 19:57 Sample: 1980M01 2011M12 Lags: 2 Null Hypothesis: Obs F-Statistic Prob. LNP does not Granger Cause LNR 382 4.28279 0.0145 LNR does not Granger Cause LNP 0.57702 0.5621 3) SOYBEANS Pairwise Granger Causality Tests Date: 09/12/12 Time: 19:57 Sample: 1980M01 2011M12 Lags: 2 Null Hypothesis: Obs F-Statistic Prob. LNP does not Granger Cause LNS 382 3.45528 0.0326 LNS does not Granger Cause LNP 0.90996 0.4034 4) WHEAT Pairwise Granger Causality Tests Date: 09/12/12 Time: 19:58 Sample: 1980M01 2011M12 Lags: 2 Null Hypothesis: Obs F-Statistic Prob. LNP does not Granger Cause LNW 382 4.39446 0.0130
  54. 54. 53 LNW does not Granger Cause LNP 1.23447 0.2922

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