- 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. 1 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. 3 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. 5 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. 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. 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. 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. 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 dont 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 Thailands 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. 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. 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 (2005w032008w20) and
fourth (2008w212010w05) 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
(2005w032008w20), and fourth (2008w212010w05) 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. Chinas 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 didnt 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. 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. 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 theres 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
Thailands 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. 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. 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. 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. 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 periods gap from the long run equilibrium. Grangers
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. 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. 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. 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. 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. 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: doesnt 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 doesnt 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. 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 doesnt exist
and the series is stationary I(0). * denotes significance at the 5%
level. 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. 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. 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 didnt 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. 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 didnt 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 didnt 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. 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 didnt 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 dont
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. 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 couldnt 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
couldnt 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. 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 didnt find cointegrating
relationship between crude oil price and price of rice, we didnt
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. 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. 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 didnt 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. 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. 36. 35 Chen, S.T., Kuo, H.I., Chen, C.C., (2010).
Modelling the relationship between the oil price and global food
prices. Applied Energy 87, 25172525 Owen, A.D., K. Chowdhury, and
J.R.R. Garrido. (1997). Price Interrelationship in the Vegetable
and Tropical Oils Market. Applied Economics 29(1997): 119-24.
Zhang, Q. and Reed, M. (2008). Examining the Impact of the World
Crude Oil Price on Chinas Agricultural Commodity Prices: The Case
of Corn, Soybean, and Pork. Selected paper for presentation at the
Southern Agricultural Economics Association Annual Meetings,
Dallas, TX, February 2nd - 5th, 2008 De Gorter, H. (2008).
Explaining Agricultural Commodity Price Increases: The Role of
Biofuel Policies. Corvalis: Oregon State University, 2008. UNCTAD
(2011). Price Formation in Financialized Commodity Markets: The
Role of Information Dickey, D A. & Fuller, W A. (1981).
Likelihood ratio statistics for autoregressive time series with a
unit root. Econometrica; 49: 105772. Ghaith, Z. and Awad I M.
(2011). Examining the Long Term Relationship between Crude Oil and
Food Commodity Prices: Co-integration and Causality, International
Journal of Economics and Management Sciences Vol. 1, No.5, 2011,
pp. 62-72. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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. 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