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International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015 851
International Journal of Energy Economics and
Policy
ISSN: 2146-4553
available at http: www.econjournals.com
International Journal of Energy Economics and Policy, 2015, 5(3), 851-868.
Empirical Analysis of Agricultural Commodity Prices, Crude
Oil Prices and US Dollar Exchange Rates using Panel Data
Econometric Methods
Anthony N. Rezitis*
Department of Economics and Management, University of Helsinki, P.O. Box 27, Latokartanokaari 9, FI-00014, Finland.
*Email: antonios.rezitis@helsinki.
ABSTRACT
This study examines the long-run relationship between crude oil prices, US dollar exchange rates (EXCR) and the prices of 30 selected international
agricultural prices and ve international fertilizer prices using panel econometric methods with and without unobserved heterogeneous effects on data
sets of the period from June 1983 to June 2013. The empirical results indicate that in the long-run the impact of crude oil price changes on agricultural
prices is positive and statistically signicant, while the impact of US dollar EXCR changes is negative and statistically signicant. Furthermore, the
effect of US dollar EXCR changes on commodity prices is stronger than that of crude oil price changes. The present study estimates the speed of
adjustment of agricultural commodity prices (AGCP) towards the long-run equilibrium and the empirical results indicate that AGCP adjust slowly
towards the long-run equilibrium. Furthermore, the results of this study indicate that when unobserved heterogeneous effects with common factors are
considered, the effects of oil prices and US dollar EXCRs on AGCP are much weaker than in the case in which such effects are not considered. Finally,
the persistent movements of agricultural prices are mostly attributed to the rst common factor, which is closely related to the US dollar EXCR, while
the short-lived deviations of AGCP away from their long-run equilibrium level might be due to the remaining four stationary common factors, which
are capturing factors affecting the world supply and demand conditions of the international agricultural prices.
Keywords: Agricultural Commodity Prices, Oil Prices, Exchange Rates, Panel Cointegration, Panel Error Correction, Unobserved Heterogeneity,
Common Factors
JEL Classications: O13, C01, C32
1. INTRODUCTION
Since the middle of 2000s, the world witnessed a remarkable
increase of agricultural and fertilizer prices which has been
coincided with an increase in world oil prices and a decline in
the value of the US dollar (Figure 1). In particular, crude oil
affects agricultural commodity (AGCP) production and thus
AGCP through input prices (i.e. cost-push effects), since their
production may depend in the use of crude oil. Furthermore,
more increasingly recently, crude oil prices potentially affect
at least some agricultural commodities (e.g. grains, sugar and
vegetable oils) through competition in output markets for bio-fuel
production. In other words, high crude oil prices make bio-fuel
production more protable and this causes increases in the prices
of agricultural commodities used in bio-fuel production.
Since many agricultural commodities are priced in US dollars in
international markets, a weaker dollar may increase the demand for
agricultural commodities of foreign consumers and thus the prices
of agricultural commodities. Note, that the price impact of the
demand shift of agricultural commodities may be particularly large
since it is believed that the demand and supply of these commodities
are price inelastic. Another reason of the inverse relationship
between AGCP and the US dollar exchange rate (EXCR) may be
ination. Investors and speculators invest in agricultural commodity
futures when the US dollar depreciates because they are concerned
about high ination rates, thus driving up agricultural commodity
and food prices (Rezitis and Sassi, 2013).
The purpose of this study is to examine the long-run relationship
between crude oil prices, US dollar EXCR and the prices of
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015
852
Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
30 selected world agricultural commodities (and ve fertilizer
commodities). In order to analyze the relation between crude oil
prices, US EXCR, and AGCP (as well as fertilizer prices), panel
data econometric methods are employed on commodity price
data sets based on monthly observations from June 1983 to June
2013. In particular, seven price data sets which are presented
in Table 1 are used in the present study, of which the st is
consisted of 30 AGCP, the second of six cereal prices (CERL),
the third of 10 vegetable oil and protein meals prices (VOPM),
the forth of cotton, bananas oranges and sugar prices (CBOS),
the fth of six meat and seafood prices (MASE), the sixth of
four beverage prices (BEVE) and the seventh of ve fertilizer
prices (FERT).
The panel econometric methods used in the present study attempt
to capture the long-run dynamics between the series under
consideration as well as the speed of adjustment towards the
long-run equilibrium of AGCP in the case that these prices are
found to be away from the long-run equilibrium. In particular,
the present study uses panel econometric methods with and
without unobserved cross-sectional dependence due to common
factors (Baltagi, Ch. 12, 2008; Banerjee and Wagner, 2009;
Verbeek, Ch. 10, 2012) to estimate the long-run equilibrium
relationship between AGCP, crude oil prices and US dollar
EXCR. The classical non-stationary panel data methods consider
unobserved cross-sectional dependence with the use of dummy
variables or with certain assumptions about the error term.1
Moreover, unobserved heterogeneity across cross-sectional
units is assumed to remain constant through time within each
cross-sectional unit. More recent panel methods consider
unobserved heterogeneity across cross-sectional units with the
use of common factors and, thus, unobserved heterogeneity is
allowed to have heterogeneous time trends across cross-sectional
units. It has been shown that neglecting such effects may lead
to serious biases in parameter estimates and wrong inference.
1 In this paper, the terminology “classical non-stationary panel data methods”
refers to the “rst-generation panel methods” (Verbeek, Ch. 10, p. 412,
2012)
The empirical results indicate that signicant price dynamics
exist in the long-run between the series under consideration
and that AGCP adjust slowly towards the long-run equilibrium.
An interesting nding of the present study is that the effects of
crude oil prices and dollar EXCR on international agricultural
prices become weaker when the unobserved heterogeneity across
cross-sectional units with the use of common factors is taken
into consideration.
This study contributes to the related literature in several ways.
First, it is the rst study to use panel econometric methods
with and without unobserved heterogeneous effects, which are
modeled by the factor structure to examine the long-run price
dynamics between 30 AGCP (and ve fertilizer prices) as well as
subgroups of these commodities, crude oil prices and US dollar
EXCR. Thus, the present study is able to compare and contrast
the results provided by the two aforementioned panel econometric
approaches. Among the previous literature, only two studies
(i.e., Chen et al., 2010; Nazlioglou and Soytas, 2012) use similar
methods to examine international commodity price dynamics.
More specically, the study by Nazlioglou and Soytas (2012) uses
only classical non-stationary panel methods (i.e., without a factor
structure) to examine the relationship between 24 AGCP, world
oil prices and the US dollar, while the study by Chen et al. (2010)
uses only panel econometric methods with common factors to
examine the price dynamics of 51 tradable commodities. Second,
among the classical non-stationary panel techniques used by
the present study, the approach of Pesaran et al. (1997; 1999) is
used to estimate the error correction structure of the international
agricultural prices, crude oil prices and US dollar EXCR, while the
study by Nazlioglou and Soytas (2012) uses the traditional Engle
and Granger (1987) approach modied in a panel framework.
More specifically, this approach falls into the category of
traditional pool estimators (e.g., random-effects and xed-effects
estimators), in which the intercepts are allowed to differ across
units while all the other estimated coefcients and error variances
are constrained to be the same across units. On the other hand, the
panel error correction model used in the present study allows the
short-run coefcients and error variances to change among units
(i.e., AGCP), thus allowing the dynamic specication to differ
across units. Third, the panel error correction approach used in the
present study (Pesaran et al., 1997; 1999) is a one-step estimation
approach that is based on the estimation of an autoregressive
distributed lag (ARDL) equation in which the short- and long-
run coefcients are estimated simultaneously. Fourth, the present
paper not only captures cross-sectional dependence across the
individual commodity prices with the use of common factors by
using the approaches of Bai (2009) and Kneip et al. (2012), but it
also estimates the direct effects of crude oil prices and US EXCR
on commodity prices. On the other hand, the study by Chen et al.
(2010), while considering cross-sectional dependence and the
factor structure by using the methodology of Bai and Ng (2004),
does not estimate the direct effects of oil prices and US EXCR on
commodity prices. Finally, the panel data econometric approaches
used in the present study provide more and better information
than the simple time series methods because the former derives
information from both time and cross-sectional dimensions, but
the latter only from the time dimension.
Figure 1: Agricultural commodity price index (2005=100), crude oil
price (US dollar per barrel), US dollar exchange rate index (2010=100)
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015 853
Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
The remainder of this paper is organized as follows. Section 2 presents
and discusses the literature on the linkages of AGCP, oil prices and US
dollar EXCR, focusing mainly on the long-run relationships between
the aforementioned series. Section 3 presents the empirical model and
the data, while Section 4 provides the econometric methods and the
empirical results. Conclusions are drawn in Section 5.
2. LITERATURE REVIEW
The paper by Rezitis and Sassi (2013) reviews several studies
analyzing factors inuencing food prices. Among these factors are
energy and fertilizer prices (Abbott et al., 2008; Mitchell, 2008;
Trostle, 2008); neglected investment in R and D and infrastructure
Table 1: Data description: Agricultural commodity, fertilizer, petroleum prices and EXCR
No. Commodity Description Unit
1-30: AGCP
1-6: Cereals (CERL)
1 Barley (BARL) Canadian no. 1 Western Barley US dollars per metric ton
2Corn (CORN) U.S. No. 2 Yellow, FOB Gulf of Mexico US dollars per metric ton
3Rice (RICE) 5% broken milled white rice, Thailand nominal price quote US dollars per metric ton
4Sorghum (SORG) U.S. No. 2 milo yellow, FOB Gulf ports US dollars per metric ton
5Wheat (WHEH) U.S. No. 1 Hard Red Winter, ordinary protein, FOB Gulf of Mexico US dollars per metric ton
6 Soft Red Winter Wheat
(WHES)
U.S. No. 2, export price delivered at the US Gulf port for prompt or 30 days
shipment
US dollars per metric ton
7-16: VOPM
7Coconut oil (COCO) Coconut oil (Philippines/Indonesia), bulk, CIF Rotterdam US dollars per metric ton
8Fishmeal (FISM) Peru sh meal/pellets 65% protein, CIF US dollars per metric ton
9Groundnuts (GRON) 40/50 (40 to 50 count per ounce), CIF Argentina US dollars per metric ton
10 Olive oil (OLIO) Extra virgin less than 1% free fatty acid, ex-tanker price U.K. US dollars per metric ton
11 Palm oil (PALO) Malaysia palm oil futures (rst contract forward) 4-5% FFA US dollars per metric ton
12 Peanut oil (PEAO) Any origin, CIF Rotterdam US dollars per metric ton
13 Soybean meal (SOYM) Chicago soybean meal futures (rst contract forward) minimum 48% protein US dollars per metric ton
14 Soybean oil (SOYO) Chicago soybean oil futures (rst contract forward) exchange approved grades US dollars per metric ton
15 Soybeans (SOYB) Chicago soybean futures contract (rst contract forward) No. 2 yellow and par US dollars per metric ton
16 Sunower (SUNF) US export price from Gulf of Mexico US dollars per metric ton
17-20: CBOS
17 Cotton (COTT) Cotlook “A Index,” middling 1-3/32 inch staple, CFR far eastern ports US cents per pound
18 Bananas (BANA) Central American and Ecuador, FOB U.S. Ports US dollars per metric ton
19 Oranges (ORAN) Miscellaneous oranges, CIF French import price US dollars per metric ton
20 Sugar (SUGA) Free market, CSCE contract No. 11 nearest future position US cents per pound
21-26: Meat and seafood (MASE)
21 Beef (BEEF) Australian and New Zealand 85% lean fores, CIF U.S. import price US cents per pound
22 Lamb (LAMB) Lamb, frozen carcass Smitheld London US cents per pound
23 Pork (PORK) 51-52% lean Hogs, U.S. price US cents per pound
24 Poultry (POUL) Whole bird spot price, ready-to-cook, whole, iced, Georgia docks US cents per pound
25 Fish (salmon) (SALM) Farm Bred Norwegian Salmon, export price US dollars per kilogram
26 Shrimp (SHRI) No. 1 shell-on headless, 26-30 count per pound, Mexican origin, New York port US cents per pound
27-30: Beverages (BEVE)
27 Cocoa Beans (COCB) International Cocoa Organization cash price, CIF US and European ports US dollars per metric ton
28 Coffee Arabica (COFA) International Coffee Organization New York cash price, ex-dock New York US cents per pound
29 Coffee Robusta (COFR) International Coffee Organization New York cash price, ex-dock New York US cents per pound
30 Tea (TEA) Mombasa, Kenya, Auction Price. From July 1998, Kenya auctions, Best Pekoe
Fannings. Prior, London auctions, c.i.f. U.K. warehouses
US cents per kilogram
31-35: Fertilizer (FERT)
31 DAP Standard size, bulk, spot, f.o.b. US Gulf US dollars per metric ton
32 Potassium chloride
(muriate of potash) (POTA)
Standard grade, spot, f.o.b. Vancouver US dollars per metric ton
33 Phosphate rock (Morocco)
(PHOS)
70% BPL, contract, f.a.s. Casablanca US dollars per metric ton
34 TSP Up to September 2006 bulk, spot, f.o.b. US Gulf; from October 2006 onwards
Tunisian, granular, f.o.b.
US dollars per metric ton
35 Urea (UREA) Bulk, spot, f.o.b. Black Sea (primarily Yuzhnyy) beginning July 1991; for
1985-91 (June) f.o.b. Eastern Europe
US dollars per metric ton
36. Crude oil (OILP)
Crude oil (petroleum)
(OILP)
Simple average of three spot prices; Dated Brent, West Texas Intermediate, and
the Dubai Fateh
US dollars per barrel
37. EXCR
EXCR Real effective US dollar EXCR Narrow index (2010=100)
Source: Items No. 1-No. 36 are obtained from: http://www.indexmundi.com/commodities/, Item No. 37 is obtained from http://www.bis.org/statistics/eer/. CSCE: Coffee sugar and cocoa
exchange, DAP: Diammonium phosphate, TSP: Triple superphosphate, EXCR: Exchange rates, CBOS: Cotton, bananas oranges and sugar prices, VOPM: Vegetable oil and protein meals
prices, AGCP: Agricultural commodity prices
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015
854
Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
(Abbott et al., 2008); high oil prices (Abbott et al., 2008); shocks
in production (Schnepf, 2008); emerging economics and structural
change in global demand (Headey and Fan, 2008); depreciation
of the US dollar (Mitchell, 2008; Trostle, 2008; Abbott et al.,
2011); inelastic markets (Abbott et al., 2011); import policies
(Wright, 2009; Abbott et al., 2011); low level of global inventories
(Wright, 2009; 2011); global bio-fuels production (Mitchell, 2008;
Abbott et al., 2008; Wright, 2009; Headey and Fan, 2008; Abbott
et al., 2011); and export policies (Trostle, 2008). Moreover, the
paper discusses related literature (e.g. Robles et al., 2009; Cooke
and Robles, 2009; Gilbert, 2010; Timmer, 2009) on the role of
bio-fuels and speculation on food and agricultural commodity
markets. The empirical part of the paper uses a structural time
series approach to examine the behavior of the monthly commodity
food prices for the period from January 1992 to October 2012. The
results support that commodity food prices show cyclicality and
seasonality and that US real effective EXCR has a negative effect
on commodity food prices while crude oil price has a positive
effect. Furthermore, the impact (in absolute value) of crude oil
price on commodity food prices is smaller (i.e. 0.0399) than the
impact of the US EXCR (i.e. −0.7868).
The paper by Nazlioglou and Soytas (2012) examines the dynamic
relationship between oil price, US dollar EXCR and 24 world
agricultural commodities in a panel framework using classical
panel cointegration and causality analysis for the period from
January 1980 to February 2010. The empirical results on panel
cointegration indicate that the impact of an increase in the oil prices
is positively signicant in all individual agricultural commodities
except in the case of cotton and coffee. Furthermore, the impact of
a decline in the value of the US dollar is positive in all individual
AGCP except in the case of coconut oil, cacao, and coffee. With
regard to the panel coefcients, AGCP are positively correlated
with the oil prices with an estimated coefcient of 0.25, and are
negatively correlated with the US dollar EXCR with an estimated
coefcient between −0.71 and −0.72.
The paper by Pala (2013) investigates the linkage between food
price index and crude oil price index, using Johansen cointegration
test, and Granger causality in a vector error correction model
(VECM) framework for the period from January 1990 to
August 2011. The empirical results indicate the presence of
two structural breaks, after August 2008 and November 2008.
Cointegration regression coefcient between the crude oil and
food price variables is negative at the full sample and at the period
from January 1990 to August 2008 while positive at the period
from November 2008 to August 2011.
The study by Ghaith and Awad (2011) uses cointegration analysis
to investigate long-run relationships between the prices of crude
oil and several food commodities (e.g. maize, wheat, sorghum,
soybean, barley, linseed oil, soybean oil, and palm oil) for the
period from January 1980 to December 2009. The results indicate
that there is strong evidence of long-run relationship between crude
oil and food commodity prices.
The work by Ciaian and Kancs (2011) investigates the
interdependences between the energy, bio-energy and food prices.
The paper uses a time series cointegration mechanism to nine
major AGCP such as corn, wheat, rice, sugar, soybeans, cotton,
banana, sorghum and tea, along with one average crude oil price for
the period January 1994-December 2008. The empirical ndings
show that the prices of all nine aforementioned agricultural
commodities are cointegrated with crude oil price especially during
the sub-period January 2004-December 2008. Furthermore, the
results show that an increase in oil price by 1 $/barrel increases
the AGCP between 0.10 $/barrel and 1.80 $/barrel.
The paper by Saghaian (2010) presents empirical results using a
VEC system to investigate the long-run relationships between oil,
ethanol, corn, soybeans, and wheat price. The empirical results
from the VEC system supports ve cointegrating equations and
that the speed of adjustment coefcients show overshooting of each
commodity price series indicating that the price system quickly
adjusts to its long-run equilibrium.
The study by Zhang et al. (2010) uses price data on fuels
(i.e. ethanol, gasoline and oil), and agricultural commodities
(i.e. corn, rice, soybeans, sugar and wheat) to investigate the
long-run cointegration of these prices using a VECM. The results
indicate no direct long-run price relations between fuels and
agricultural prices and limited short-run relationship between
fuels and agricultural prices.
The study by Chen et al. (2010) analyzes the relationship between
the prices of corn, soybeans and wheat, and the crude oil price.
The empirical results show that the change in each one of the
aforementioned grain prices is signicantly inuenced by the
change in the crude oil price as well as by the change of other
grain prices.
The paper by Frank and Garcia (2010) using weekly data from
1998 to 2008 investigates the linkages between several AGCP
(i.e. wheat, corn, cattle and hogs), EXCR, and oil prices by
employing value at risk (VAR) and VECM methods. The paper
identies a break point which divides the sample period into two
sub-periods (i.e. 1998-2006 and 2006-2009). The empirical results
of this study show that for the rst sub-period the crude oil price
and the EXCR have limited effect on AGCP, while for the second
sub-period the effects of the crude oil prices and the EXCR on
agricultural prices are much stronger.
The paper by Chen et al. (2010) performs common factor
analysis on a panel of 51 international commodity prices from
January 1980 to December 2009. The study uses the Panel Analysis
of Non-stationarity in Idiosyncratic and Common Components
procedure developed by Bai and Ng (2004) and identies two
common factors for commodity prices. The results indicate that the
rst common factor is non-stationary, while the second common
factor is stationary. The graphical evidence shows that the rst
common factor is a mirror image of the US EXCR. Thus, the study
concludes that the highly persistent movements of commodity
prices are mainly attributed to the rst common component,
which is closely related to the US EXCR, while the stationarity
of the second common factor implies short-lived deviations from
equilibrium price dynamics reecting changes in the world demand
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015 855
Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
and supply conditions in accordance with prices theories (Kellard
and Wohar, 2006; Wang and Tomek, 2007).
The study by Harri et al. (2009) examines the relationship between
AGCP (i.e. corn, soybeans, soybean oil, cotton and wheat), EXCR
and oil prices using cointegration analysis for the period from
January 2000 to September 2008. The empirical results indicate
that corn, cotton, and soybean prices are related to oil prices but
wheat prices are not. EXCR are related to all aforementioned
commodity prices.
The study by Arshad and Hameed (2009) examines the relationship
between crude oil prices and cereal prices (i.e. maize, rice and
wheat) using data of the period from January 1980 to March
2008. This paper uses the Engle–Granger two-stage estimation
approach and Granger causality tests. The empirical results support
the presence of a unidirectional long-run causality from crude oil
prices to the three cereal prices. The study by Hameed and Arshad
(2009) investigates potential linkages between petroleum prices
and vegetable oil prices (i.e. palm oil, soybean oil, sunower
oil, and rapeseed oil) for the period from January 1983 to March
2008 using the Engle–Granger two-stage estimation approach
and Granger causality tests. The empirical results show that in
the long-run there is a one direction relationship from crude oil
price to the prices of each of the four vegetable oils. The reverse
is not true, i.e. crude oil price is not inuenced by the price of
any of the vegetable oils under consideration. Furthermore, the
speed of adjustment of palm oil, rapeseed oil, soybean oil, and
sunower oil prices to their long-run levels equaled 0.017, 0.032,
0.032 and 0.034, respectively, indicating a very slow adjustment
of each one of the aforementioned commodities towards the long-
run equilibrium.
3. MODEL AND DATA
Based on the aforementioned discussions AGCP can be modeled
as a function of oil prices and EXCR. The empirical model in the
log-log form is presented as follows:
ln ln ln
AGCP tOILPEXCR
it ii it
it
it
=+++ +
αδ ββ ε
12 (1)
For i = 1,…,N; t = 1983:06-2013:06
Where AGCPit is referred to the price of the agricultural commodity
i (i = 1,…,30 Table 1) at time t (t = 1983:06-2013:06), OILP is
the world crude oil price, and EXCR is the real effective US dollar
EXCR. The parameter αi is a xed-effect parameter while β1ι and
β2ι are the slope parameters and the term διt indicates deterministic
time trends which are specic to individual units (members or
cross-sections) of the panel. Notice that a similar empirical model
can be applied for analyzing fertilizer prices (FERT) and any one
of the ve subgroups of agricultural prices as they are presented
in Table 1, i.e., cereals (CERL), VOPM, CBOS, meat and seafood
(MASE) and beverages (BEVE).
The data used in this study consists of monthly observations of the
period from June 1983 to June 2013 of 30 AGCP, ve fertilizer
prices, the world crude oil prices and the real effective US dollar
EXCR. Table 1 provides a detailed description of the data. It is
worth stating that agricultural commodity and fertilizer price data
have been converted into the same unit of measurement, i.e. dollar
per metric ton, in order to avoid data potential inconsistency
generated for measuring prices in different units.
4. EMPIRICAL METHODS AND RESULTS
The empirical methods used in the present study include, rst,
panel unit root tests (i.e. Harris and Tzavalis, 1999; Im et al., 2003;
Levin et al., 2002) to provide information about the stationarity
properties of the variables under consideration. Second, panel
cointegration tests (i.e. Pedroni, 1997; 1999) are performed to
ascertain the presence of cointegration and then the estimation
of long-run cointegration parameters is carried out based on the
studies by Pedroni (2001; 2007). Third, panel error correction
estimation is performed based on the study by Pesaran et al.
(1999), which presents three alternative pooled estimates, i.e. mean
group (MG), pooled MG (PMG) and dynamic xed-effects (DFE)
estimators. Finally, a panel data analysis with unobservable
heterogeneous effects based on the studies by Bai (2009) and Kneip
et al. (2012) is conducted to deal with the potential problem of the
unobserved heterogeneity. Note that the panel unit root tests, the
panel cointegration tests and the panel error correction estimation
utilize the Regression Analysis of Time Series procedures found in
Doan (2012), while the unobserved heterogeneity estimation uses
the R-package procedures developed by Bada and Liebl (2014).
It is worth stating that even though the data set used in the present
study is not purely panel in nature, since the crude oil prices and
EXCR do not change across the different types of agricultural
commodities, this study uses panel data econometric techniques
to analyze the long-run relationship between international
AGCP, crude oil prices and EXCR. This is because the panel
data econometric approaches used in the present paper derive
information from both the time and the cross-sectional dimension
of the AGCP and combine them with the time dimension of the
crude oil prices and the EXCR. Since, however, the data set used
in the present paper is not purely panel in nature, the information
content is rather limited. For this reason, the present study, in
addition to the classical non-stationary panel methods (i.e., panel
unit roots, panel cointegration and error correction models), uses
panel data approaches with unobservable heterogeneous effects
and a factor structure.
4.1. Panel Unit Root Analysis
Panel unit root tests provide information about the order of
integration of the variables under consideration which is
crucial in empirical analysis since applying the ordinary least
square estimator in non-stationary variables results in spurious
regressions. The present study employs three different panel
unit root tests in order to test the order of integration of the
variables. The rst test is the one developed by Levin et al.
(2002, henceforth LLC), the second is the Harris and Tzavalis
(1999, henceforth, HT), and the third is the Im et al. (2003,
henceforth IPS). Most of the panel unit root tests use the
following general structure:
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015
856
Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
∆∆
yy
yd
it iitiL
L
p
it Lmim
ti
t
i
=+
++
−
=
−
∑
ρθ
αε
,,,1
1 (2)
m = 1,2,3
Where, Δ is the rst difference operator, p is the lag length, dmt is a
vector of deterministic variables and αmt the corresponding vector
of coefcients for models m = 1, 2, and 3 where d1t = {empty set},
d2t = {1} and d3t = {1, t}, correspondingly. ρi = 0 indicates that the
y process has a unit root for individual i, while ρi < 0 indicates
a stationary process. According to LLC (2002), since ρi is xed
across i the alternative hypothesis is that the ρι are identical and
negative. A similar but simpler test is derived for (2) by HT (1999)
when the time dimension of the panel is relatively short, with a null
hypothesis of a unit root and an alternative with a single stationary
value. Unlike the two aforementioned tests, the IPS (2003) test
allows the ρi to vary and in fact the null hypothesis implies that
all series have a unit root, i.e. ρi = 0 for all i, while the alternative
hypothesis indicates that some of the series are stationary, i.e.,
ρi < 0 for some i.
The panel unit root test results are presented in Tables 2 and 3.
Most of the panel unit root results show a tendency of failing to
reject the null hypothesis of panel unit root for the levels of the
variables.2 On the contrary, most of the results indicate rejection of
the null of panel unit root of the rst-differences of the variables
in support of the alternative of stationary rst-differences of the
variables. Thus, from the panel unit root analysis, it could be
concluded that the variables are integrated of order one, suggesting
a possible long-run cointegrating relation among each one of the
AGCP such as lnAGCP, lnCERL, lnVOPM, lnCBOS, lnMASE,
lnBEVE, and lnFERT with the oil price, lnOILP, and the EXCR,
lnEXCR, variables. Thus, the next step of the empirical analysis
investigates the presence of cointegration between AGCP and oil
price and EXCR.
4.2. Panel Cointegration Analysis
In this section, a number of studies by Pedroni (1997; 1999;
2001; 2007) are used in order to test and estimate panel
cointegration among the variables in question. These studies
allow not only differing short-run dynamics but also differing
cointegrating vectors. The panel cointegration test developed by
Pedroni (1997; 1999) is used to test the existence of the long-run
equilibrium relationship among the variables. In particular, the
testing procedure species a null hypothesis indicating that the
series are not cointegrated, that is, that the residuals from (1) are
still I(1). More specically, if the alternative is that the series are
cointegrated and have a common cointegrating vector, then the
null is that the series are not cointegrated or they are cointegrated
but do not have a common cointegrating vector. Table 4 presents
the results of the seven different statistics developed by Pedroni
(1997; 1999). Of these seven statistics, four are based on pooling
2 Note that the paper by Rezitis (2014) used a panel VAR approach (in levels)
rather than a panel error correction model for investigating the relationship
between oil prices, US exchange rates and agricultural commodity prices.
This was done because some of the panel unit root tests rejected the null of
unit root for the levels of the variables.
along the within-dimension (panel cointegration statistics) and
the remaining three are based on pooling along the between-
dimension (group mean panel cointegration statistics). The
panel cointegration statistics are based on estimators that pool
the autoregressive coefcient across different units for the unit
root tests on the estimated residuals, while the group mean panel
cointegration statistics are based on estimators that average the
individually estimated coefcients for each unit i. With regard to
the rst set of statistics, three of the four statistics (panel v-statistic,
panel ρ-statistic, and panel Phillips and Perron [PP] - statistic) use
non-parametric corrections analogous to the work of Phillips and
Perron (1988), while the fourth (panel augmented Dickey-Fuller
[ADF] - statistic) is a parametric ADF t-statistic. In the second
set of statistics, two of the three statistics (group ρ-statistic, and
group PP-statistic) are based on non-parametric corrections while
the third (group ADF - statistic) is an ADF based test statistic.
Let’s denote by γι the autoregressive coefcient of the residuals
in the ith unit then the null and alternative hypothesis of the panel
statistics are specied as follows:
H0: γi = 1, for all i,
HA: γi = γ < 1, for all i (3)
By contrast the hypothesis of the group statistics are described as:
H0: γi = 1, for all i,
HA: γi < 1, for all i (4)
Note that the alternative hypothesis of the within-dimension
(panel) statistics presumes a common value for γi = γ, while the
Table 2: Results of panel unit root LLC test
(1983:06-2013:06)
Variables None Constant Constant
and trend
Variables in levels
lnAGCP 2.25 [0.985] 1.94 [0.974] 3.66 [0.999]
lnCERL 1.06 [0.848] 1.56 [0.941] 1.45 [0.92]
lnVOPM 1.05 [0.854] 1.01 [0.843] 1.55 [0.940]
lnCBOS 0.52 [0.701] 0.89 [0.814] 2.07 [0.981]
lnMASE 1.88 [0.970] 1.13 [0.871] 3.21 [0.999]
lnBEVE −0.36 [0.357] 0.30 [0.621] 1.44 [0.926]
lnFERT 1.09 [0.862] 1.31 [0.905] 2.06 [0.981]
lnOILP 3.68 [0.999] 6.29 [1.00] 2.45 [0.992]
lnEXCR −4.36 [0.00] −2.85 [0.002] 1.71 [0.957]
Variables in differences
ΔlnAGCP −23.5 [0.00] −54.7 [0.00] −14.8 [0.00]
ΔlnCERL −26.5 [0.00] −14.5 [0.00] −10.0 [0.00]
ΔlnVOPM −35.1 [0.00] −21.7 [0.00] −17.5 [0.00]
ΔlnCBOS −18.9 [0.00] −5.91 [0.00] −2.09 [0.018]
ΔlnMASE −22.3 [0.00] −3.93 [0.00] 1.23 [0.892]
ΔlnBEVE −15.8 [0.00] −1.42 [0.077] 2.42 [0.999]
ΔlnFERT −16.0 [0.00] −1.14 [0.125] 2.84 [0.998]
ΔlnOILP −50.5 [0.00] −6.01 [0.00] 6.03 [1.00]
ΔlnEXCR −67.8 [0.00] −45.6 [0.00] −35.5 [0.00]
LLC: Levin, Lin and Chu (Levin et al., 2002) panel unit root test. Δ is the difference
operator. Numbers in brackets are P values, VOPM: Vegetable oil and protein meals
prices, AGCP: Agricultural commodity prices, EXCR: Exchange rates, CBOS: Cotton,
bananas oranges and sugar prices
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015 857
Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
between-dimension (group) statistics do not presume a common
value for γi = γ and allow an additional source of potential
heterogeneity across individual units of the panel.
The results of panel cointegration tests presented in Table 4 are
obtained with and without the inclusion of time dummies. All the
test statistics reject the null hypothesis of no cointegration between
AGCP (fertilizers), oil prices and EXCR. Furthermore, the panel
cointegration tests reject the null hypothesis of no cointegration
for all subgroups of AGCP except in the cases of MASE (meat
and seafood) and BEVE (beverages). In the case of MASE the
test results obtained with the inclusion of time dummies fail to
reject the null of no cointegration while the test results obtained
without the inclusion of time dummies support the presence of
cointegration. With regards to BEVE one of the test results (panel
v-statistic) obtained with the inclusion of time dummies support
the presence of cointegration, while three out of seven of the
test results (panel v-statistic, group ρ- statistic, and group ADF-
statistic) obtained without the inclusion of dummy dummies
support the presence of cointegration. In general, the panel
cointegration test results support the presence of cointegration
among the variables under consideration which implies that prices
converge to their long-run equilibrium by correcting any deviation
from the long-run equilibrium in the short-run.
Since the panel cointegration tests indicate the presence
of cointegration relationships among the variables under
consideration then the next step is the estimation of the long-run
parameters. Based on Pedroni (2001; 2007) two estimators are
used for estimating the long-run parameters of the cointegration
Table 3: Results of panel unit root HT and IPS tests (1983:06-2013:06)
Variables HT test IPS test
None Constant Constant and trend Constant Constant and trend
Variables in levels
lnAGCP 0.23 [0.594] −7.59 [0.00] −5.36 [0.00] −1.42 [0.076] −3.60 [0.00]
lnCERL 0.23 [0.594] −0.61 [0.267] −1.21 [0.111] −0.10 [0.456] −0.96 [0.166]
lnVOPM 0.26 [0.602] −1.33 [0.091] −0.60 [0.272] −1.22 [0.111] −2.78 [0.002]
lnCBOS 0.03 [0.513] −9.43 [0.00] −9.62 [0.00] −1.03 [0.151] −1.61 [0.053]
lnMASE 0.04 [0.518] −6.43 [0.00] −4.14 [0.00] −1.04 [0.148] −0.48 [0.314]
lnBEVE −0.01 [0.494] −2.39 [0.008] 0.07 [0.526] −1.66 [0.048] −1.21 [0.112]
lnFERT 0.37 [0.646] 1.10 [0.866] 0.70 [0.759] −0.003 [0.49] −2.23 [0.013]
lnOILP 1.14 [0.874] 2.96 [0.998] −1.95 [0.025] 6.00 [1.00] −2.63 [0.004]
lnEXCR −0.20 [0.418] −4.12 [0.00] 2.32 [0.990] −4.96 [0.00] −0.13 [0.445]
Variables in differences
ΔlnAGCP −1159.9 [0.00] −511.8 [0.00] −318.9 [0.00] −31.1 [0.00] −30.5 [0.00]
ΔlnCERL −480.7 [0.00] −212.2 [0.00] −132.1 [0.000] −20.7 [0.00] −13.2 [0.00]
ΔlnVOPM −564.7 [0.00] −248.9 [0.00] −154.6 [0.00] −16.2 [0.00] −29.9 [0.00]
ΔlnCBOS −486.3 [0.00] −214.7 [0.00] −134.0 [0.00] −14.6 [0.00] −14.6 [0.00]
ΔlnMASE −553.6 [0.00] −244.3 [0.00] −152.4 [0.00] −20.3 [0.00] −14.5 [0.00]
ΔlnBEVE −398.2 [0.00] −175.4 [0.00] −109.2 [0.00] −10.3 [0.00] −9.98 [0.00]
ΔlnFERT −346.4 [0.00] −152.8 [0.00] −94.6 [0.00] −12.9 [0.00] −12.5 [0.00]
ΔlnOILP −1050.4 [0.00] −463.7 [0.00] −288.3 [0.00] −42.2 [0.00] −42.9 [0.00]
ΔlnEXCR −1007.4 [0.00] −443.8 [0.00] −275.6 [0.00] −55.3 [0.00] −24.3 [0.00]
HT indicates the Harris and Tzavalis (1999) panel unit root test while IPS indicates the Im, Pesarant and Shin (Im et al., 2003) panel unit root test. Δ is the difference operator. Numbers in
brackets are P values. VOPM: Vegetable oil and protein meals prices, AGCP: Agricultural commodity prices, EXCR: Exchange rates, CBOS: CBOS: Cotton, bananas oranges and sugar prices
Table 4: Panel cointegration test (1983:06-2013:06)
Variables Panel Group
v-statistic ρ-statistic PP-statistic ADF-statistic ρ-statistic PP-statistic ADF-statistic
Cointegration test-with time dummies
ln AGCP, lnOILP, lnEXCR 8.42*** −3.98*** −3.30*** −3.54*** −7.15*** −5.24*** −6.08***
lnCERL, lnOILP, lnEXCR 8.66*** −7.72*** −5.55*** −5.97*** −7.27*** −5.76*** −6.40***
lnVOPM, lnOILP, lnEXCR 7.67*** −4.10*** −3.10*** −3.63*** −5.07*** −4.07*** −4.88***
lnCBOS, lnOILP, lnEXCR 8.11*** −6.52*** −4.30*** −4.48*** −9.57*** −5.92*** −6.69***
lnMASE, lnOILP, lnEXCR 1.10 0.07 −0.14 −0.07 0.63 0.24 0.12
lnBEVE, lnOILP, lnEXCR 2.64*** −1.18 −1.10 −1.36 −1.15 −1.22 −1.59
lnFERT, lnOILP, lnEXCR 6.02*** −3.33*** −2.40** −2.53** −2.51** −2.25** −2.63***
Cointegration test-without time dummies
lnAGCP, lnOILP, lnEXCR 9.92*** −7.35*** −5.64*** −6.62*** −10.5*** −7.56*** −9.56***
lnCERL, lnOILP, lnEXCR 4.15*** −4.08*** −3.11*** −4.03*** −3.22*** −2.84*** −3.95***
lnVOPM, lnOILP, lnEXCR 5.98*** −3.67*** −2.75*** −3.31*** −3.90*** −3.20*** −3.98***
lnCBOS, lnOILP, lnEXCR 9.27*** −8.94*** −5.58*** −6.52*** −12.2*** −7.34*** −9.33***
lnMASE, lnOILP, lnEXCR 2.57** −2.29** −1.90** −1.87* −2.48** −2.00** −2.09**
lnBEVE, lnOILP, lnEXCR 1.90* −0.92 −0.85 −1.34 −1.65* −1.29 −2.10**
lnFERT, lnOILP, lnEXCR 4.42*** −4.51*** −3.16*** −4.13*** −4.22*** −3.42*** −4.67***
***,**,*Indicate statistical signicance at 1%, 5% and 10% level of signicance, respectively. The statistics are standard normally distributed asymptotically. VOPM: Vegetable oil and
protein meals prices, AGCP: Agricultural commodity prices, EXCR: Exchange rates, CBOS: Cotton, bananas oranges and sugar prices
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015
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Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
relationships given by Equation (1). These estimators are
the fully-modified least squares (FMLS) which was firstly
developed by Phillips and Hansen (1990) and Hansen (1992)
and the dynamic ordinary least squares (DOLS) which was also
proposed independently by Stock and Watson (1993). Note that
the least squares estimated parameters in Equation (1) suffer from
simultaneity bias due to the correlation between the left-hand side
variable (lnAGCPit) and the error term (εit) and from dynamic
endogeneity due to serial correlation of the error term (εit). The
FMLS estimator used in estimating (1) corrects for the bias of
the estimated parameters, while the DOLS estimator deals with
the endogeneity by adding the current, lags and leads of the rst
difference of the right-hand variables (lnOILP, lnEXCR) to the
regression of Equation (1).3
Tables 5-7 present the results of the panel fully modied ordinary
least squares (FMOLS) and DOLS estimators. In particular, Table 5
presents panel cointegration coefcients for the AGCP as a group
as well as for each specic agricultural commodity (components)
price i (i = 1,…,30 Table 1). In an analogous manner, Table 6
presents the results for each AGCP sub-group while Table 7
shows the results corresponding to the fertilizer group as well
3 For the DOLS, one lag and one lead are used. A number of different lags
and leads were tried but it was found that the estimates are not sensitive
to the selection of the lag and lead length. Note also that both the Akaike
information criterion and the Schwarz Bayesian criterion support the
aforementioned lag and lead length.
as to each specic fertilizer price component. Furthermore, all
the aforementioned tables are accompanied by heterogeneity
tests (χ2-tests) for the estimated coefcients
αδ
ββ
ii
ii
^^
^^
,, ,
12
corresponding to the variables under consideration (intercept, time,
lnOILPi, lnECXPi). The null hypothesis of the heterogeneity test is
that each individual coefcient is equal to the average of the group.
An inspection of the empirical results presented in Tables 5-7
indicates that FMOLS and DOLS estimators produce very similar
results in terms of the magnitude and statistical signicance of
the parameter estimates for both the average group price and the
individual price components.
4.2.1. Agricultural commodities (AGCP)
The third row of Table 5 presents the estimated parameters of
the cointegration vector corresponding to the panel, i.e. whole
group of AGCP. These estimates indicate that in the long-run
the average AGCP responds positively (about 0.32) to the crude
oil price (OILP) and negatively (about −0.74) to the U.S. EXCR
at conventional levels of signicance. Note that AGCP shows a
higher response to the EXCR changes rather than to the OILP
changes. The same Table 5 indicates that all individual price
components respond positively (except OLIO, LAMB, POUL,
and SHRI) to the crude oil price changes and negatively (except
SHRI, COCB and TEA) to the U.S. EXCR at conventional levels of
signicance. Notice that although each of the COCO, FISM, PALO,
Variables Panel FMOLS Panel DOLS
Intercept Trend lnOILP lnEXCR Intercept Trend lnOILP lnEXCR
lnAGCP 8.8136***
(0.1913)
−0.0003***
(0.0001)
0.3104***
(0.0090)
−0.7119***
(0.0406)
8.9315***
(0.1934)
−0.0004***
(0.0001)
0.3193***
(0.0094)
−0.7414***
(0.0411)
lnBARL 6.3188***
(0.8334)
0.0016***
(0.0003)
0.2980***
(0.0394)
−0.6496***
(0.1766)
6.2885***
(0.8444)
0.0015***
(0.0003)
0.3006***
(0.0410)
−0.6435***
(0.1794)
lnCORN 7.0916***
(1.0325)
−0.0005*
(0.0003)
0.4488***
(0.0488)
−0.7922***
(0.2188)
7.3385***
(1.0243)
−0.0006**
(0.0003)
0.4624***
(0.0498)
−0.8516***
(0.2176)
lnRICE 11.5539***
(1.0288)
−0.0003
(0.0003)
0.3744***
(0.0486)
−1.5135***
(0.2180)
11.8586***
(1.0252)
−0.0005*
(0.0003)
0.3927***
(0.0498)
−1.5878***
(0.2178)
lnSORG 6.9754***
(0.9282)
−0.0002
(0.0003)
0.3969***
(0.0439)
−0.7520***
(0.1967)
7.1749***
(0.9250)
−0.0003
(0.0003)
0.4078***
(0.0450)
−0.8000***
(0.1965)
lnWHEH 8.3720***
(0.8371)
−0.0002
(0.0003)
0.3723***
(0.0396)
−0.9628***
(0.1774)
8.5291***
(0.8430)
−0.0003
(0.0003)
0.3871***
(0.0410)
−1.0035***
(0.1791)
lnWHES 9.3143***
(0.8791)
−0.0006**
(0.0003)
0.3901***
(0.0415)
−1.1790 ***
(0.1863)
9.5281***
(0.8764)
−0.0007**
(0.0003)
0.4098***
(0.0426)
−1.2346***
(0.1862)
lnCOCO 7.3150***
(1.5049)
−0.0008
(0.0005)
0.4779***
(0.0711)
−0.5049
(0.3189)
7.3035***
(1.5126)
−0.0009*
(0.0005)
0.4859***
(0.0735)
−0.5058
(0.3213)
lnFISM 5.6575***
(1.0561)
−0.0002
(0.0003)
0.5530***
(0.0499)
−0.1967
(0.2238)
5.9346***
(1.0441)
−0.0003
(0.0003)
0.5698***
(0.0507)
−0.2653
(0.2218)
lnGRON 8.7990***
(0.9832)
−0.0005*
(0.0003)
0.3820***
(0.0465)
−0.6799***
(0.2084)
8.8799***
(0.9935)
−0.0006**
(0.0003)
0.3818***
(0.0483)
−0.6959***
(0.2110)
lnOLIO 12.8388***
(1.0241)
0.0021***
(0.0003)
−0.1488***
(0.0484)
−0.9920***
(0.2171)
12.6666***
(1.0441)
0.0022***
(0.0003)
−0.1607***
(0.0507)
−0.9486***
(0.2218)
lnPALO 6.3950***
(1.4877)
0.0004
(0.0005)
0.3962***
(0.0703)
−0.3731
(0.3153)
6.3725***
(1.5331)
0.0003
(0.0005)
0.4054***
(0.0745)
−0.3724
(0.3257)
lnPEAO 7.5486***
(1.0193)
0.0005*
(0.0003)
0.3860 ***
(0.0482)
−0.4431**
(0.2160)
7.6308***
(1.0423)
0.0004
(0.0003)
0.3980***
(0.0507)
−0.4660**
(0.2214)
lnSOYM 9.6910***
(0.9042)
0.00001
(0.0003)
0.2807***
(0.0427)
−1.1171***
(0.1916)
9.8888***
(0.9111)
−0.00003
(0.0003)
0.2822***
(0.0443)
−1.1596
(0.1935)
Table 5: Panel cointegration coefcients (1983:06‑2013:06): AGCP prices, oil price and US EXCR
Condt...
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015 859
Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
PORK and COFA prices show a negative response to the EXCR
changes, however, these responses are statistically insignicant
at any conventional level of signicance. The heterogeneity tests
for the estimated coefcients presented in the ve last rows of
Table 5 reject the hypothesis of equality of the individual estimated
coefcient to the corresponding average panel (group) coefcient
presented in the third row of the Table 5.
4.2.2. Cereals (CERL)
Table 6 presents panel cointegration coefcients referred to the
responses of the whole group of cereal prices with respect to the
crude oil price and to the U.S. EXCR. The results indicate that the
average cereal price (CERL) responds positively (about 0.39) to
the OILP and negatively (about −1.0) to the EXCR at conventional
levels of signicance. Table 5 supports that all individual cereal
prices respond positively to the OILP changes at conventional
levels of signicance. The heterogeneity test of Table 6, however,
indicates that individual cereal price responses to OILP changes
are not statistically signicantly different than the average cereal
price at any conventional level of signicance. Furthermore,
all individual cereal prices (Table 5) respond negatively to the
EXCR at conventional levels of signicance. With regards to the
Variables Panel FMOLS Panel DOLS
Intercept Trend lnOILP lnEXCR Intercept Trend lnOILP lnEXCR
lnSOYO 8.8506***
(1.0171)
−0.0006**
(0.0003)
0.4588***
(0.0481)
−0.8473***
(0.2156)
8.9844***
(1.0315)
−0.0008***
(0.0003)
0.4756***
(0.0501)
−0.8839***
(0.2191)
lnSOYB 8.9482***
(0.9300)
−0.0006**
(0.0003)
0.3890***
(0.0440)
−0.9902***
(0.1971)
9.1189***
(0.9341)
−0.0006**
(0.0003)
0.3982***
(0.0454)
−1.0307***
(0.1984)
lnSUNF 9.6869***
(1.0523)
−0.0001
(0.0003)
0.4303***
(0.0497)
−0.9852***
(0.2230)
9.7912***
(1.0658)
−0.0001
(0.0003)
0.4477***
(0.0518)
−1.0157***
(0.2264)
lnCOTT 12.4737***
(1.0401)
−0.0015***
(0.0003)
0.2665***
(0.0492)
−1.2385***
(0.2204)
12.6637***
(1.0647)
−0.0015***
(0.0003)
0.2670***
(0.0517)
−1.2790***
(0.2262)
lnBANA 8.9948***
(0.8937)
0.0006**
(0.0003)
0.2654***
(0.0422)
−0.8011***
(0.1894)
9.2716***
(0.8795)
0.0005*
(0.0003)
0.2858***
(0.0427)
−0.8716***
(0.1868)
lnORAN 8.3603***
(0.8596)
0.0014***
(0.0003)
0.2555***
(0.0406)
−0.6724***
(0.1822)
8.4873***
(0.8816)
0.0013***
(0.0003)
0.2673***
(0.0428)
−0.7049***
(0.1873)
lnSUGA 16.8693***
(1.2187)
0.0005
(0.0004)
0.2183***
(0.0576)
−2.6311***
(0.2583)
17.4375***
(1.2194)
0.0005
(0.0004)
0.2144***
(0.0593)
−2.7529***
(0.2590)
lnBEEF 10.8946***
(0.6090)
−0.0010***
(0.0002)
0.3336***
(0.0288)
−0.8689***
(0.1291)
11.1236***
(0.5981)
−0.0011***
(0.0002)
0.3467***
(0.0291)
−0.9242***
(0.1271)
lnLAMB 9.5923***
(0.6869)
0.0017***
(0.0002)
−0.0859***
(0.0325)
−0.3612**
(0.1456)
9.4446***
(0.6900)
0.0017***
(0.0002)
−0.0913***
(0.0335)
−0.3280**
(0.1466)
lnPORK 6.9498***
(0.9963)
−0.0035***
(0.0003)
0.4558***
(0.0471)
−0.1083
(0.2112)
7.1037***
(1.0083)
−0.0037***
(0.0003)
0.4751***
(0.0490)
−0.1497
(0.2142)
lnPOUL 7.8000***
(0.2635)
0.0025***
(0.0001)
−0.0141
(0.0125)
−0.2174***
(0.0559)
7.8204***
(0.2649)
0.0025***
(0.0001)
−0.0137
(0.0129)
−0.2212***
(0.0563)
lnSALM 14.6938***
(0.7593)
−0.0033***
(0.0002)
0.3800***
(0.0359)
−1.4811***
(0.1609)
14.7812***
(0.7432)
−0.0034***
(0.0002)
0.3883***
(0.0361)
−1.5031***
(0.1579)
lnSHRI 4.9683***
(0.7136)
0.0004**
(0.0002)
−0.2958***
(0.0337)
0.3263**
(0.1512)
4.9150***
(0.7048)
0.0005**
(0.0002)
−0.3182***
(0.0343)
0.3501**
(0.1497)
lnCOCB 3.4497***
(1.1384)
−0.0009**
(0.0004)
0.4472***
(0.0538)
0.5616**
(0.2413)
3.5362***
(1.1399)
−0.0010**
(0.0004)
0.4607***
(0.0554)
0.5344**
(0.2422)
lnCOFA 9.1578***
(1.6538)
−0.0016***
(0.0005)
0.3973***
(0.0782)
−0.5075
(0.3505)
9.2619***
(1.6996)
−0.0017***
(0.0006)
0.4186***
(0.0826)
−0.5409
(0.3610)
lnCOFR 9.8579***
(1.8875)
−0.0038***
(0.0006)
0.5336***
(0.0892)
−0.7689**
(0.4000)
10.0293***
(1.9370)
−0.0039***
(0.0006)
0.5537***
(0.0941)
−0.8153**
(0.4115)
lnTEA 4.9905 ***
(0.8002)
−0.0001
(0.0003)
0.2685***
(0.0378)
0.3890**
(0.1696)
4.7806***
(0.8056)
−0.0002
(0.0003)
0.2813***
(0.0391)
0.4281**
(0.1711)
Heterogeneity test (
χ
29
2 ‑test) for the estimated coefcients
Intercept 273.28
[0.000]
291.37
[0.000]
Trend 1320.56
[0.000]
1308.00
[0.000]
lnOILP 1058.09
[0.000]
1066.51
[0.000]
lnEXCR 311.00
[0.000]
334.62
[0.000]
Numbers in parenthesis are standard errors while those in brackets are P values. ***,**,*indicate statistical signicance at 1%, 5% and 10% level of signicance, respectively.
VOPM: Vegetable oil and protein meals prices, AGCP: Agricultural commodity prices, EXCR: Exchange rates, FMOLS: Fully modied ordinary least squares, DOLS: Dynamic ordinary
least squares
Table 5: (Continued)
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015
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Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
Table 6: Panel cointegration coefcients and heterogeneity tests by specic commodity subgroup (1983:06‑2013:06): CERL,
VOPM, CBOS, MASE, BEVE
Variables Panel FMOLS Panel DOLS
Intercept Trend lnOILP lnEXCR Intercept Trend lnOILP lnEXCR
Panel cointegration
coefcients
lnCERL 8.2709***
(0.3784)
−0.00005
(0.0001)
0.3801***
(0.0178)
−0.9748***
(0.0801)
8.4530***
(0.3782)
−0.0001
(0.0001)
0.3934***
(0.0184)
−1.0202***
(0.0803)
lnVOPM 8.5730***
(0.3531)
0.00003
(0.00011)
0.3605***
(0.0167)
−0.7129***
(0.0749)
8.6571***
(0.3577)
−0.00003
(0.0001)
0.3683***
(0.0173)
−0.7343***
(0.0759)
lnCBOS 11.6745***
(0.5065)
0.0003
(0.0002)
0.2514***
(0.0239)
−1.3358***
(0.1073)
11.9650***
(0.5106)
0.0002
(0.0002)
0.2586***
(0.0248)
−1.4021***
(0.1085)
lnMASE 9.1498***
(0.2882)
−0.0005***
(0.0001)
0.1289***
(0.0136)
−0.4518***
(0.0611)
9.1981***
(0.2872)
−0.0006***
(0.0001)
0.1311***
(0.0140)
−0.4627***
(0.0610)
lnBEVE 6.8640***
(0.7174)
−0.0016***
(0.0002)
0.4117***
(0.0339)
−0.0815
(0.1520)
6.9020***
(0.7327)
−0.0017***
(0.0002)
0.4286***
(0.0356)
−0.0984
(0.1556)
Heterogeneity tests (
χ
5
2-test)
for the estimated coefcients
lnCERL 20.24
[0.001]
43.37
[0.000]
6.49
[0.260]
12.61
[0.027]
22.10
[0.000]
43.46
[0.000]
7.24
[0.203]
14.32
[0.013]
lnVOPM 31.20
[0.000]
58.66
[0.000]
138.59
[0.000]
17.94
[0.035]
28.33
[0.000]
59.51
[0.000]
138.47
[0.000]
17.16
[0.046]
lnCBOS 39.52
[0.000]
45.52
[0.000]
0.52
[0.913]
43.31
[0.000]
42.26
[0.000]
40.02
[0.000]
0.96
[0.808]
46.12
[0.000]
lnMASE 118.45
[0.000]
945.26
[0.000]
404.72
[0.000]
92.51
[0.000]
126.66
[0.000]
942.98
[0.000]
424.94
[0.000]
101.73
[0.000]
lnBEVE 13.85
[0.003]
34.63
[0.000]
12.47
[0.005]
13.41
[0.003]
14.12
[0.002]
32.67
[0.000]
11.97
[0.007]
13.93
[0.002]
Numbers in parenthesis are standard errors while those in brackets are P values. ***,**,*indicate statistical signicance at 1%, 5% and 10% level of signicance, respectively.
VOPM: Vegetable oil and protein meals prices, CBOS: Cotton, bananas oranges and sugar prices, FMOLS: Fully modied ordinary least squares, DOLS: Dynamic ordinary least squares
Table 7: Panel cointegration coefcients and heterogeneity tests (1983:06‑2013:06): Fertilizer (FERT) prices, oil price and
US EXCR
Variables Panel FMOLS Panel DOLS
Intercept Trend lnOILP lnEXCR Intercept Trend lnOILP lnEXCR
Panel cointegration
coefcients
lnFERT 7.9124***
(0.5380)
0.0007***
(0.0002)
0.5863***
(0.0254)
−1.0949***
(0.1140)
7.9124***
(0.5380)
0.0007***
(0.0002)
0.5863***
(0.0254)
−1.0949***
(0.1140)
lnDAP 8.1293***
(1.0900)
0.0001
(0.0003)
0.5899***
(0.0515)
−1.0093***
(0.2310)
8.2916***
(1.1044)
−0.0001
(0.0004)
0.6144***
(0.0537)
−1.0563***
(0.2346)
lnPOTA 7.2824***
(1.2188)
0.0025***
(0.0004)
0.4320***
(0.0576)
−0.9069***
(0.2583)
7.5917***
(1.2040)
0.0023***
(0.0004)
0.4604***
(0.0585)
−0.9875***
(0.2558)
lnPHOS 6.1097***
(1.5150)
0.0008*
(0.0005)
0.6246***
(0.0716)
−0.9476***
(0.3211)
6.3559***
(1.5134)
0.0006
(0.0005)
0.6524***
(0.0735)
−1.0137***
(0.3215)
lnTSP 8.2544***
(1.1108)
0.0007*
(0.0004)
0.5311***
(0.0525)
−1.0620***
(0.2354)
8.4056***
(1.1273)
0.0006
(0.0004)
0.5489***
(0.0548)
−1.1033***
(0.2395)
lnUREA 9.7862***
(1.0169)
−0.0006**
(0.0003)
0.7539***
(0.0481)
−1.5487***
(0.2155)
9.9007***
(1.0104)
−0.0008***
(0.0003)
0.7834***
(0.0491)
−1.5874***
(0.2146)
Heterogeneity test (
χ
5
2-test)
for the estimated coefcients
Intercept 4.91
[0.296]
4.48
[0.343]
Trend 39.19
[0.000]
38.54
[0.000]
lnOILP 20.60
[0.000]
20.40
[0.000]
lnEXCR 5.19
[0.268]
4.81
[0.307]
Numbers in parenthesis are standard errors while those in brackets are P values. ***,**,* indicate statistical signicance at 1%, 5% and 10% level of signicance, respectively.
DAP: Diammonium phosphate, TSP: Triple superphosphate, EXCR: Exchange rates
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015 861
Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
coefcients of EXCR, heterogeneity test (Table 6) indicates that
individual cereal price responses are statistically signicantly
different than the average cereal price response at the 5% level
of signicance. In particular as indicated in Table 5, the highest
response (in absolute value) presents RICE (about −1.58) followed
by WHES (about −1.2).
4.2.3. VOPM
Table 6 shows panel cointegration results related to the whole
group of vegetable oils and protein meal. The cointegration
parameters for the whole group of the aforementioned category
indicate that the average price of VOPM responds positively
(about 0.36) to the OILP and negatively (about −0.73) to the
EXCR at conventional levels of signicance. As indicated in
Table 5, all individual VOPM prices (except OLIO) respond
positively to the OILP changes at conventional levels of
signicance with FISM showing the highest response (about
0.56). Furthermore, the heterogeneity test (Table 6) indicates that
individual vegetable oils and protein meal price responses to OILP
changes are statistically signicantly different than the average
vegetable oils and protein meal prices at any conventional level
of signicance. All individual VOPM prices (Table 5) respond
negatively to the EXCR at conventional levels of signicance,
except for the cases of COCO, FISM, and PALO prices which
do not show any statistical signicant response to EXCR changes
at any conventional level of signicance. The heterogeneity test
(Table 6) indicates that individual vegetable oils and protein meal
price responses to the EXCR changes are statistically signicantly
different than the average vegetable oils and protein meal prices
at the 5% level of signicance.
4.2.4. CBOS
Table 6 presents coefcients referred to the responses of the
whole group of CBOS prices with respect to the crude oil price
and to the U.S. EXCR. The average CBOS price shows a positive
response (about 0.25) to the OILP and negative (about −1.4) to
the EXCR at conventional levels of signicance. As indicated
in Table 5, all individual prices respond positively to the OILP
changes at conventional levels of signicance. The heterogeneity
test (Table 6), however, indicates that individual CBOS price
responses to OILP changes are not statistically signicantly
different than the average CBOS price at any conventional
level of signicance. Moreover, all individual CBOS prices
(Table 5) respond negatively to the EXCR at conventional levels
of signicance, with SUGA showing the highest (in absolute
value) response (about −2.7) following by COTT (about −1.2).
The heterogeneity test (Table 6) indicates that individual CBOS
price responses to the EXCR changes are statistically signicantly
different than the average CBOS prices at the 5% level of
signicance.
4.2.5. Meat and seafood (MASE)
Table 6 presents panel cointegration coefcients for the group
of meat and seafood prices. In particular, the average MASE
price presents a positive response (about 0.13) to the OILP and
negative (about −0.46) to the EXCR at conventional levels of
signicance. As indicated in Table 5, among individual prices
BEEF, PORK and SALM respond positively and statistically
signicant at conventional levels of signicance to the OILP,
while although LAMB, SHRI and POUL show negative responses
only the rst two are statistically signicant at conventional levels
of signicance. All individual prices (Table 5) respond negatively
(except SHRI) and statistically signicant at conventional level
of significance (except PORK) to the EXCR changes. The
heterogeneity tests (Table 6) indicate that individual MASE
price responses to the OILP and EXCR changes are statistically
signicantly different than the average MASE prices at any
statistical level of signicance.
4.2.6. Beverages (BEVE)
Table 6 shows panel cointegration coefcients for the group of
beverage prices. The average BEVE price presents a positive
and statistical signicant response (about 0.42) to the OILP and
a negative (about −0.09) but statistical insignicant effect to
the EXCR. All individual prices (Table 5) show a positive and
statistical signicant response to OILP at conventional levels of
signicance. Among individual prices COFA and COFR show
negative responses to EXCR changes with only the response of
COFR to be statistically signicant at the 5% level. Furthermore,
the prices of COCH and TEA present a positive and statistically
signicant response to EXCR changes at conventional levels
of signicance. The heterogeneity tests (Table 6) indicate that
individual BEVE price responses to the OILP and EXCR changes
are statistically signicantly different than the average BEVE price
changes at any statistical level of signicance.
4.2.7. Fertilizers (FERT)
Finally, Table 7 presents panel cointegration results for the whole
group of fertilizers as well as for individual fertilizer prices.
The average FERT price shows a positive response (about 0.58)
to the OILP and a negative (about −1.09) to the EXCR at any
conventional levels of signicance. All individual prices (Table 7)
show a positive response to OILP and a negative response to
EXCR at any conventional level of signicance. Furthermore, the
heterogeneity test (Table 7) indicates that the individual FERT
price responses to the OILP changes are statistically signicantly
different than the average FERT price response at any statistical
level of signicance. The heterogeneity test (Table 7), however,
indicates that the individual FERT price responses to EXCR
changes are statistically insignicantly different than the average
FERT price response at any statistical level of signicance.
4.3. Panel Error Correction Analysis
The usual practice of generating panel error estimates is either
to estimate separate regressions for each individual unit of the
panel and calculate the coefcient means, which is called the
MG estimator, or to pool the data and assume that the slope
coefcients and error variances are identical. The studies by
Pesaran et al. (1997; 1999), however, proposed an intermediate
procedure, the PMG estimator, which constraints long-run
coefcients to be identical across individual units of the panel
but allows short-run coefcients and error variances to change
among units. There are several reasons to assume the long-
run equilibrium relationships between variables to be similar
across individual units of the panel, due to arbitrage conditions,
common weather and technologies affecting all units in a similar
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015
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Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
way. The present study computes and presents MG, PMG and
DFE estimators for the variables under consideration. Note that
the DFE estimator constraints all of the slope coefcients and
the error variances to be the same across all individual units of
the panel.
Let’s assume that the long-run relationship between AGCP, crude
oil price and EXCR is similar to Equation (1). Then the following
ARDL(1,1,1) equation is used:
ln ln ln
ln ln
,
AGCP OILP OILP
EXCR
it ii ti t
iti
=+ +
+
−
−
µδ δ
δδ
10 11 1
20 21 1EEXCRAGC
Pu
ti it it
−−
++
11
λ
ln ,
(5)
And the error correction equation becomes:
∆
∆
ln ln ln ln
ln
,
AGCP AGCP OILP EXCR
it it ii ti t
i
=−−−
()
−
−
φθθθ
δ
10
12
11 OOILP EXCRu
ti tit
−+
δ
21 ∆ln
(6)
Where,
θµ
λ
01
i
i
i
=−,
θ
δδ
λ
1
10 11
1
i
ii
i
=+
−,
θ
δδ
λ
2
20 21
1
i
ii
i
=+
−,
φλ
ii
=− −
()
1
Note that the error correction Equation (6) is written in terms of
current, rather than lagged levels of exogenous variables. The
DFE approach can be applied in estimating Equation (5) and the
long-run estimated coefcients are provided in Equation (6).
The MG estimator assumes that all the coefcients of Equation (6)
are heterogeneous and they are estimated by least squares for each
individual unit of the panel. Then the coefcients of the individual
regressions are pooled by averaging, which provides the MG
estimates. Note that, the estimated model given by Equation (6)
is linear in the variables but non-linear in the parameters. In the
MG estimation approach, model (6) is estimated in the linear form
and then the non-linear coefcients are derived. In particular, the
linear form of Equation (6) is given as:
∆
∆
ln ln ln ln
l
,
'' '
AGCP AGCP OILP EXCR
it it ii ti t
i
=−−− −
−
φθθθ
δ
10
12
11 nnlnOILP EXCRu
ti tit
−+
δ
21 ∆
(7)
Then θ0i, θ1i and θ2i are obtained as follows:
θθ
φθθ
φθθ
φ
0
0
1
1
2
2
i
i
i
i
i
i
===
'
''
,, .
(8)
Finally the PMG estimator is more complicated relative to the
MG estimator. It xes the long-run coefcients (θ0i, θ1i and θ2i) and
allows the short-run coefcients (δ11i and δ21i) to vary across the
individual units of the panel. It uses an iterative procedure which
solves the rst order conditions for the two sets of parameters
(homogeneous vs. heterogeneous) given the other.
Table 8 presents the three aforementioned pooled estimates.4
More specically, the MG estimate which does not impose any
restrictions, the PMG estimate which imposes common long-
run coefcients and the DFG estimate which imposes common
slope coefcients and error variances across the individual units
of the panel. The results of Table 8 indicate that the long-run
coefcients as well as the speed of adjustment coefcient have the
expected signs and they are statistically signicant at conventional
levels of signicance for the three alternative pooled estimation
approaches (MG, PMG and DFE). Furthermore, the response of
AGCP is higher to EXCR change rather than to the OILP change.
In particular, these estimates indicate that in the long-run AGCP
responds positively (between 0.327 and 0.405) to the OILP
and negatively (between −1.132 and −1.380) to the EXCR at
conventional levels of signicance. Comparing the present results
to those discussed in the previous subsection and particularly to
those presented in the third row of Table 5 it can be seen that
they are close with respect to the response of AGCP to the OILP
changes but the present results show higher response of AGCP
to EXCR changes.
On the contrary to the empirical model of the previous subsection
(Pedroni, 2001; 2007) the empirical models of the present
subsection (MG, PMG and DFE) provide estimates of the speed
of adjustment coefcients because they estimate error correction
models. Note, that the MG estimator suggests faster adjustment
(about −0.055) than the PMG or DFE estimators (−0.046 and
−0.037 respectively). The reason is that imposing homogeneity
restrictions causes an upwards bias in the coefcient of the lagged
dependent variable, and thus the MG estimator shows a higher
4 The models were estimated with a longer lag order but the estimates were
not sensitive to the inclusion of additional lags. This is also supported by
Pesaran et al. (1999), who indicate that the coefcients are robust to the lag
order, especially in the case of large T (time). It should also be noted that
when additional lags were included they were found to be insignicant.
Furthermore, diagnostic tests of the residuals of the estimated models
indicate that there is no evidence of autocorrelation and heteroskedasticity.
Furthermore, the inclusion of seasonal dummies did not show any evidence
of seasonality. Finally, to check the robustness, the models were re-
estimated with shorter time spans, i.e. the rst 5 years of the data and/or the
last 5 years were omitted, and the empirical results showed a high degree of
robustness.
Table 8: Alternative pooled estimates for ARDL (1,1,1)
AGCP prices (1983:06-2013:06): MG, PMG and DFE
Variables MG PMG DFE
lnOILP 0.327***
(7.227e-159)
0.405***
(0.021)
0.341***
(0.030)
lnEXCR −1.132***
(4.425e-158)
−1.380***
(0.139)
−1.332***
(0.204)
Speed of
adjustment (ϕ)
−0.055***
(9.793e-160)
−0.046**
(0.021)
−0.037***
(0.003)
Log likelihood 14484.95 14444.50 12741.99
Number of estimated
parameters
210 152 36
The error correction term does not include an intercept because the intercept is allowed to
vary, while the slopes of the error correction parameters are constrained to be xed (Doan,
2012). Numbers in parenthesis are standard errors. ***,**indicate statistical signicance
at 1%, and 5% level of signicance, respectively. MG: Mean group, PMG: Pooled mean
group, DFE: Dynamic xed-effects, AGCP: Agricultural commodity prices
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015 863
Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
adjustment than the PMG or DFE estimators (Pesaran et al., 1999).
Overall the results of Table 8 indicate that the average adjustment
coefcient seems to be about −0.046 indicating that it will take
about 21.74 months for the AGCP to close the gap between the
actual price level and the long-run equilibrium price level.
Table 9 provides DFE estimates for each component of the
AGCP group (CERL, VOMP, CBOS, MASE and BEVE) as
well as for the group of fertilizer (FERT) prices. All estimated
coefcients have the expected sign and they are statistically
signicant at all conventional levels of signicance (except
the coefficients of EXCR in the BEVE and MASE price
components). The results indicate that the response of each
one of the agricultural price components and fertilizer price,
presented in Table 9, is higher to the EXCR change rather than
to the OILP change. Furthermore, among the agricultural price
components CERL and VOMP show the highest responses
(about 0.435 each one of them) to the OILP and MASE shows
the lowest response (about 0.131). Moreover, CERL shows
the highest response (about −1.809) to the EXCR, followed by
VOMP and CBOS (of about −1.798 and −1.607 respectively)
while MASE and BEVE do not show any statistical signicant
response. With regards to the speed of adjustment coefcients,
CBOS shows the highest adjustment (about −0.101) while
BEVE shows the lowest (about −0.024). Finally, comparing the
long-run estimated coefcients of Table 9 to those discussed in
the previous subsection and specically to those presented in
Tables 6 and 7 it can be seen that the coefcients corresponding
to the OILP are close, while the coefcients of the present
subsection corresponding to the EXCR are much higher than
those of the previous subsection, except in the case of MASE
where it is statistically insignicant.
4.4. Panel Data Analysis with Unobserved
Heterogeneous Effects
This subsection examines the relationship between crude oil
prices, US dollar EXCR and international agricultural prices by
considering unobserved heterogeneity, in a panel framework,
which is modeled by a factor structure. Classical panel data
models incorporate unobserved heterogeneity with the use of
dummy variables or with structural assumptions regarding the
error term. Furthermore, the unobserved heterogeneity is assumed
to remain constant though time within each cross-sectional
unit. In recent studies on panel data analysis, such as Ahn et al.
(2013); Bai (2009); Kneip et al. (2012) and Pesaran (2006),
unobserved individual effects are allowed to have heterogeneous
(i.e., individual-specic) time trends that can be approximated by
a factor structure. Based on the studies by Bai (2009) and Kneip
et al. (2012), Model (1) becomes:
ln ln lnAGCP OILP EXCR
it it ti
ti
t
=+ ++
++
µα ββ
νε
12 (9)
For i = 1,…,N; t = 1983:06-2013:06
Where, μ is the intercept, αi are time-constant individual effects
of individual commodity i (i = 1,…,30 Table 1) and vit are time-
varying individual effects of individual commodity i (i = 1,…,30
Table 1) for time period t (t = 1983:06-2013:06), which are
assumed to be generated by d common time-varying factors. Two
specications of the time-varying individual effects are used in
the present study. The rst is the specication proposed by Kneip
et al. (2012) and is given by:
νλ
ii
ll
l
d
tf
t
()
=
()
=
∑1 (10)
The second specication is proposed by Bai (2009) and is given by:
νλ
it il lt
l
d
==
∑
f
1 (11)
Note that f1(t) and flt are the unobserved common factors for the
models of Kneip et al. (2012) and Bai (2009), respectively, while
λil are unobserved individual loading parameters and d is the
unknown factor dimension.
The approach of Kneip et al. (2012) consists of a two-step
estimation procedure. First, the common slope parameters (β1
and β2), the intercept (μ), the time-constant individual effects
(αi) and the time-varying individual effects (vi(t)) are obtained
semi-parametrically. Second, the functional principal component
approach is employed to estimate the common factors f1(t),…, fd(t)
and to re-estimate the time-varying individual effects (vi(t)) more
efciently. This approach considers the case in which the common
factors f1(t) show relatively smooth patterns through time. It
includes positively auto-correlated stationary as well as non-
stationary factors. Furthermore, the time-varying individual effects,
vi(t), are approximated by smooth non-parametric functions and
Equation (9) becomes a semi-parametric model that is estimated
using the aforementioned two-step estimation procedure. It also
should be noted that since the vector of explanatory variables in
Table 9: DFE estimates for ARDL (1,1,1) AGCP components and fertilizers (1983:06-2013:06)
Variables CERL VOMP CBOS MASE BEVE FERT
lnOILP 0.435***
(0.042)
0.435***
(0.052)
0.283***
(0.047)
0.131***
(0.064)
0.384***
(0.125)
0.773***
(0.048)
lnEXCR −1.809***
(0.289)
−1.798***
(0.364)
−1.607***
(0.311)
−0.385
(0.418)
−0.138
(0.791)
−2.332***
(0.331)
Speed of adjustment (ϕ) −0.051***
(0.006)
−0.033***
(0.004)
−0.101***
(0.011)
−0.034***
(0.006)
−0.024***
(0.005)
−0.049***
(0.005)
Log likelihood 2951.58 4757.26 1054.19 2856.12 1765.45 2422.91
Number of estimated parameters 12 16 10 12 10 11
Numbers in parenthesis are standard errors. ***indicates statistical signicance at the 1%, level of signicance. AGCP: Agricultural commodity prices, CBOS: Cotton, bananas oranges
and sugar prices, EXCR: Exchange rates
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015
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Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
model (9) is allowed to contain an intercept (μ), the time-varying
individual effects (vi(t)) are centered around a common intercept
term for each specic time point and are not centered around zero.
Kneip et al. (2012) propose a sequential testing procedure based
on the KSS.C test statistic to estimate the factor dimension d.
The null hypothesis (H0) of the KSS.C test statistic is that d = 0,
while the alternative hypothesis (H1) is d = 1,2,3,… until H0
cannot be rejected. The estimated dimension is given by the
smallest dimension d, which rejects H0. The dimensionality
KSS.C test statistic of Kneip et al. (2012) can be used for non-
stationary as well as stationary factors, but it ignores factors that
are weakly auto-correlated and thus the number of factors can be
underestimated. To overcome this problem, Bai and Ng (2002)
propose four directionality tests (i.e. PC1, PC2, PC3 and BIC3).
The BIC3 test seems to perform well when the errors are cross-
correlated. It has been shown that the aforementioned four tests
might underestimate the true variance and for this reason Bai and
Ng (2002) propose three additional directionality criteria (i.e. IC1,
IC2 and IC3). In order to improve the nite sample properties of
the IC1 and IC2 tests, Alessi et al. (2010) propose two rened
directionality criteria, i.e., ABC.IC1 and ABC.IC2. Furthermore,
Ahn and Horenstein (2013) suggest two additional selection
criteria, i.e. the eigenvalue ratio and growth ratio, while Bai (2004)
propose three panel criteria, i.e. IPC1, IPC2 and IPC3, to estimate
the number of unit root factors. Finally, Onatski (2010) introduces
a threshold approach, which can be used for both stationary and
non-stationary factors and is called the criterion of eigenvalue
differences.
The panel model proposed by Bai (2009), i.e., Equations (9) and (11),
is estimated with the use of the entirely updated estimators
(Eup) proposed by Bada and Kneip (2014). More specically,
this approach allows for dependency and weak forms of
heteroskedasticity in both time and cross-section dimensions
and uses an iterated least-squares approach to estimate (9) for
non-stationary deterministic trends or stationary time-varying
individual effects, vit, such as autoregressive moving average
model processes. However, this approach excludes a large
class of non-stationary processes, such as stochastic processes
with integration. Furthermore, Bai (2009) assumes that factor
dimension d is a known parameter, which is not always the case.
However, this study uses an algorithm proposed by Bada and Kneip
(2014), i.e., Eup, which is a renement of Bai’s method, in order
to estimate the number of unobserved common factors d jointly
with the remaining parameters of the model.
Table 10 presents the empirical results of three different panel
models. In particular, the second column of Table 10 presents
the empirical results of a panel model with only time-constant
individual-specic effects. The next two columns present the
empirical results of two panel models including time-constant
individual effects as well as time-varying individual unobservable
effects. More specically, the third column of Table 10 presents
empirical results based on the Kneip et al. (2012) estimation
approach, while the fourth column presents empirical results
based on the Bai (2009) estimation method. The same Table 10
presents the results of the Kneip et al. (2012) test, which tests the
presence of unobservable common factors beyond the presence of
the individual time-constant effects.5 The test results indicate that
the common factors should be included in the model.
Among the 16-factor dimensionality (d) criteria, which are
presented in Table 10, a signicant number support the presence of
ve unobserved common factors. The empirical results presented
in Table 10 are obtained by selecting ve unobservable common
factors in the estimation process. Note, however, that the empirical
results are robust to the selection of the number of common factors.
The results indicate that the effect of crude oil prices on world
AGCP is positive and statistically signicant at the 10% level of
signicance in the Kneip et al. (2012) model and at the 1% level
of signicance in the Bai (2009) model, while the effect of EXCR
is negative and statistically signicant at the 1% level in both
models. Furthermore, in the case of the Bai (2009) and Kneip
et al. (2012) models, the effect of the crude oil is much smaller in
absolute values (i.e. 0.0348 and 0.0677) than the effect of EXCR
(−0.4220 and −0.4750). It should be stated that the estimated
5 This test is based on the dimensionality criterion proposed by Kneip et al.
(2012) to test the following hypothesis: H0: d = 0 versus H1: d > 0.
Table 10: Estimation results of panel models with
time-constant additive and time-varying unobserved
individual effects (1983:06-2013:06)
Variables lnAGCPalnAGCPblnAGCPc
Intercept 8.5100***
(0.3140)
8.3400***
(0.4740)
8.4800***
(0.0027)
lnOILP 0.2740***
(0.0042)
0.0348*
(0.0181)
0.0677***
(0.0087)
lnEXCR −0.6320***
(0.0277)
−0.4220***
(0.0979)
−0.4750***
(0.0413)
Test-statistic of Kneip et al. (2012) testd: 143.15 [0.00]
Factor dimensions (d) selection criteria
PC1 - 5 5
PC2 - 5 5
PC3 - 5 5
BIC3 - 2 2
IC1 - 5 5
IC2 - 5 5
IC3 - 5 5
IPC1 - 0 0
IPC2 - 0 0
IPC3 - 0 0
ABC.IC1 - 2 -
ABC.IC2 - 2 -
KSS.C - 23 -
ED - 2 -
ER - 2 -
GR - 23 -
aThe model presented in this column includes only time-constant additive effects (αi);
bThe model presented in this column includes time-constant additive (αi) and
time-varying unobserved individual effects (vi (t)), and uses the Kneip et al. (2012)
estimation method; cThe model presented in this column includes time-constant
additive (αi) and time-varying unobserved individual effects (vit) and uses the
Bai (2009) estimation method; dThe test of Kneip et al. (2012) is testing the presence of
time-varying interactive effects; PC1-PC3, BIC3, and IC1-IC3 are the selection criteria
of Bai and Ng (2009); IPC1-IPC3 are from Bai (2004) while ABC.IC1 and ABC.IC2 are
from Alessi et al. (2010); KKS.C is the selection criterion of Kneip et al. (2012); ED is
the eigenvalue differences criterion of Onatski (2010); ER and GR are the eigenvalue
ratio and growth ratio criteria of Ahn and Horenstein (2013), respectively; Numbers in
parenthesis are standard errors while those in brackets P values. ***,*indicate statistical
signicance at 1%, and 10% level of signicance, respectively. EXCR: Exchange rates
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015 865
Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
slope coefcients of crude oil prices and EXCR obtained by
the panel data models with unobservable heterogeneous effects
and common factors are smaller, in absolute values, than those
obtained by the static panel model with only additive time-constant
xed effects (Table 10). Furthermore, these estimated slope
coefcients are smaller (in absolute values) than those obtained
by the dynamic panel models without common factors presented
in the previous subsections of the present study as well as those
obtained by the study of Nazlioglou and Soytas (2012). Table 11
presents the results of the ADF test and the panel unit root tests
(LLC and IPC) of the residuals of Kneip et al.’s (2012) estimated
model, i.e., Equations (9) and (10). The test results of Table 11
support the stationarity of the error term of the estimated model.6
The left panel of Figure 2 shows that the 30 different agricultural
commodities have considerably different time-constant levels
(i.e.,
α
i
^ where i = 1,…,30) of prices. The middle panel of Figure 2
shows the ve estimated common factors (i.e.
ft
l
^
()
, where
l = 1,…,5), while the right panel of Figure 2 presents the time-
varying individual effects. For better visualization, each one of the
ve estimated common factors is also presented alone in Figure 3.
6 Furthermore, diagnostic tests of the residuals indicate that there is no
evidence of autocorrelation and heteroskedasticity. It should also be
noted that similar stationarity and diagnostic tests were performed on
the residuals of the Bai (2009) model, i.e. Equations (9) and (11): The
test results supported stationarity and no evidence of autocorrelation and
heteroskedasticity was found.
It is calculated that the rst two common factors explain most of
the total variance (about 68.87%) of the time-varying individual
effects (i.e.,
ν
i
^
t
()
, where I = 1,…,30). More specically, 35.63%
is explained by the rst common factor and 33.24% is explained
by the second one. Furthermore, the third common factor explains
12.96%, while the fourth and fth explain about 10.13% and
8.04%, respectively.
As Figure 3 indicates, the rst estimated common factor,
ft
1
^
()
,
resembles the US EXCR. Based on Chen et al. (2010), it could be
appropriate to infer that the rst common factor and the EXCR
share information content. In other words, factors that have a
predictable effect on EXCR will have a predicable effect on
AGCP. The ADF test results presented in Table 12 indicate that
the rst common factor is non-stationary while the remaining four
are stationary. Thus, it could be inferred that the non-stationarity
(i.e. persistent movements) of the AGCP could be attributed
to the rst common factor, which is related to the EXCR, or to
factors having a predictable effect on the EXCR. The remaining
four factors may reect the stationary behavior (i.e. temporal
movements) of the AGCP around their long-run equilibrium
level. Note that the temporal deviations of prices from their
long-run equilibrium might be attributed to factors affecting the
world supply and demand conditions of international agricultural
commodities (Kellard and Wohar, 2006; Rezitis and Sassi, 2013;
Wang and Tomek, 2007).
A comparison of the ndings of the present paper with those
obtained by Chen et al. (2010) indicates that in the paper by
Chen et al. (2010) the non-stationary factor explains the largest
proportion of the variation in the panel of prices, while in the
present paper the non-stationary factor explains only about
35.63%. Note, however, that in the present paper the ADF test
indicates that the second factor, which explains about 33.24% of
the variation, is non-stationary at the 5% level of signicance.
Thus, in this case (i.e. the 5% signicant level), the non-stationary
factors explain about 68.87% of the variation in prices and thus
the results of the present study come closer to those of the study
by Chen et al. (2010).
5. CONCLUSIONS
This study examines the long-run relationship between crude
oil prices, US dollar EXCR and the prices of 30 selected world
agricultural commodities (and ve fertilizer commodities) using
panel methods on AGCP data based on monthly observations from
June 1983 to June 2013. The present study uses classical non-
stationary panel econometric methods (such as panel cointegration
and error correction models), which do not assume unobservable
cross-sectional dependence, as well as panel methods, which
Table 11: ADF and panel unit root tests (1983:06-2013:06):
Estimated residuals
ADF tests
No. ADF No. ADF No. ADF
1 −5.2514*** 11 −3.2730*** 21 −4.4636***
2 −4.0762*** 12 −6.0074*** 22 −5.4968***
3 −5.8448*** 13 −5.1881*** 23 −4.5432***
4 −4.5437*** 14 −4.6202*** 24 −4.0866***
5−4.8458*** 15 −5.4018*** 25 −5.1955***
6 −4.8921*** 16 −4.8494*** 26 −3.9122***
7 −5.1702*** 17 −5.0498*** 27 −3.8218***
8−5.3097*** 18 −4.6116*** 28 −4.4794***
9 −5.1272*** 19 −4.0907*** 29 −4.3232***
10 −5.5002*** 20 −6.1531*** 30 −4.7548***
Panel unit tests
LLC IPS
Constant Constant
and trend
Constant Constant and
trend
−14.26 [0.00] −9.39 [0.00] −17.82 [0.00] −16.11 [0.00]
ADF indicates the augmented Dickey-Fuller t-statistic with the null of nonstationarity.
LLC indicates the Levin, Lin and Chu (Levin et al., 2002) panel unit root test while IPS
indicates the Im, Pesarant and Shin (Im et al., 2003) panel unit root test. ***refers to
the case when the null hypothesis is rejected at the 1% level of signicance. Numbers in
brackets are P values
Table 12: ADF test (1983:06-2013:06): Estimated common factors
Estimated factors
ft
^
()
1
ft
^
()
2
ft
^
()
3
ft
^
()
4
ft
^
()
5
ADF −0.9865 −1.8280* −2.3208** −2.5729*** −3.3130***
ADF indicates the augmented Dickey-Fuller t-statistic with the null of non-stationarity. ***,**,*refers to the case when the null hypothesis is rejected at the 1%, 5% and 10% level of
signicance, respectively
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015
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Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
assume cross-sectional dependence due to common factors,
to estimate the long-run dynamics between the series under
consideration. It has been shown that neglecting unobserved
heterogeneity may lead to biased parameter estimates.
The empirical results of the classical panel cointegration estimation
with regard to the whole panel of the 30 AGCP indicate signicant
price dynamics. In particular, AGCP responds positively
(0.32) to the crude oil price and negatively (−0.74) to the US
EXCR. Similar results hold for the ve agricultural commodity
subgroups (i.e. CERL, VOPM, CBOS, MASE and BEVE) and for
fertilizer prices. The empirical results of the classical panel error
correction model reinforce the results of the panel cointegration
model, supporting the signicant price dynamics in the long-run
between the series under consideration. The speed of adjustment
coefcients estimated by the error correction model indicates a low
but statistically signicant speed of adjustment of AGCP. More
specically, the speed of adjustment is between −0.037 and −0.055,
indicating that only between 3.7% and 5.5% of the disequilibrium
in AGCP is corrected every month, which is a relatively low rate.
Figure 2: Left panel: Estimated time-constant individual specic effects (i.e.,
α
i
^
where i = 1,…,30). Middle panel: Estimated common factors
(i.e.,
ft
l
^
()
where l = 1,…,5). Right panel: Estimating time-varying individual effects (i.e.,
ν
i
^
t
()
where i = 1,…,30)
Figure 3: Estimated factors:
ft
1
^
()
,
ft
^
()
2,
ft
^
()
3,
ft
^
()
4and
ft
^
()
5
International Journal of Energy Economics and Policy | Vol 5 • Issue 3 • 2015 867
Rezitis: Empirical Analysis of Agricultural Commodity Prices, Crude Oil Prices and US Dollar Exchange Rates using Panel Data Econometric Methods
Among the AGCP subgroups, the highest speed of adjustment is
shown by the CBOS price subgroup, which is about −0.101, while
the lowest is given by the beverages price subgroup (BEVE) with
about −0.024.
The empirical results of the panel data method with unobserved
heterogeneous effects and a factor structure indicate statistically
signicant price dynamics among the variables under consideration
but the effects are much smaller (in absolute values) than in the
case of panel models without heterogeneous effects and common
factors. In particular, the effect of crude oil prices on AGCP is
positive and between 0.0348 and 0.0677, while the effect of EXCR
is negative and between −0.4220 and −0.4750. Furthermore, the
common factor analysis indicates the presence of ve common
factors. Among these common factors, a graphical representation
shows that the rst one has a close relation to the US EXCR.
This indicates that factors that have a predicable effect on EXCR
will have a predicable effect on AGCP. The ADF test shows
that this factor is non-stationary and thus it is inferred that the
persistent movements of AGCP could mainly be attributed to the
rst common factor (i.e. US EXCR or factors predicting the US
EXCR). The short-run deviations of agricultural prices away from
their long-run equilibrium level can be attributed to the stationary
common factors that represent changes in the world agricultural
commodity supply and demand conditions.
The ndings of the present study support the results of previous
studies, which indicate that the AGCP are positively correlated
with the oil prices and are negatively correlated with the US
dollar EXCR. The results of this study, however, indicate that
when unobserved heterogeneous effects with common factors are
considered, the effects of oil prices and EXCR on AGCP are much
weaker than in the case in which such effects are not considered.
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