This paper attempts to model the price relationship between the major exporters of wheat. The motivation of such research is to reveal whether prices are integrated and whether potential nonlinearities in price adjustment exist. Given the perception that transactions costs may be highly variable in the wheat market, the paper aims to test for the presence of cointegration in the presence of smooth transition adjustment. The results conclude that the further the prices deviate from each other, the larger will be the arbitrage and substitution that will drive the prices close to each other. However, the results suggest that the arbitrage will be limited as the various wheat prices employed in this study may be linked to highly variable transactions costs or some other form of imperfect competition.price adjustment; estar; wheat; cointegration

Ghoshray, Atanu

English

Research Papers in Economics

Ghoshray, A., 2009. Nonlinear Price Transmission in Wheat 
Export Prices. Working Paper. Bath, UK: Department of 
Economics, University of Bath, (11/09).
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Nonlinear Price Transmission in Wheat Export Prices 
 
 
Atanu Ghoshray 
 
No. 11/09 
 
 
 
BATH ECONOMICS RESEARCH PAPERS 
 
 
 
Department of Economics and International Development 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Nonlinear Price Transmission in Wheat Export Prices 
 
 
Atanu Ghoshray
1
 
University of Bath, UK 
 
 
 
Abstract  This paper attempts to model the price relationship between the major 
exporters of wheat.  The motivation of such research is to reveal whether prices are 
integrated and whether potential nonlinearities in price adjustment exist. Given the 
perception that transactions costs may be highly variable in the wheat market, the 
paper aims to test for the presence of cointegration in the presence of smooth 
transition adjustment. The results conclude that the further the prices deviate from 
each other, the larger will be the arbitrage and substitution that will drive the prices 
close to each other. However, the results suggest that the arbitrage will be limited as 
the various wheat prices employed in this study may be linked to highly variable 
transactions costs or some other form of imperfect competition. 
 
Keywords : Cointegration, ESTAR, Wheat, Price Adjustment. 
 
JEL Classification : Q13, Q17, C22 
 
 
 
                                                 
1 Email. A. Ghoshray@bath.ac.uk    Tel. +44 1225 386402 
 
  21. Introduction 
The Law of One Price (LOP hereafter) states that after conversion to a common 
currency, the price of identical goods in spatially separated markets should be the 
same. When the price for identical goods are different then there is an incentive for 
spatial arbitrage, however, deviations from the LOP can be linked with high 
transactions costs. Since independent information about transactions costs is rarely 
available, linear models have been developed which assume transactions costs are 
constant or proportional to the commodity prices over the period of study. This 
assumption is questionable in light of the potential volatility of transactions costs. 
Binkley and Harrer (1981) show that transport costs for certain commodities can be 
highly variable and may be influenced by several factors including ship sizes and 
trade volumes. Linear cointegration methods ignore the potentially important role 
played by transactions costs and are inconsistent with discontinuous trade (Baulch 
1997).  
 
Balcombe et. al., (2007) advocate threshold models which allow for a neutral band 
where prices are not equilibrium restoring but adjustment takes place outside the band 
which is synonymous to the situation where price differentials exceed transactions 
costs. However, a limitation of this approach is that the band is assumed to be 
constant which is an unduly restrictive assumption. In this note it is argued that the 
speed of adjustment is an increasing function of the size of the discrepancy; such that 
small deviations from the LOP may not be corrected through the process of 
commodity arbitrage, but larger discrepancies are expected to be mean reverting. The 
presence of transactions costs implies a nonlinear process characterized as an 
exponential smooth transition autoregressive (ESTAR) model. In this case, 
adjustment takes place in every period, but the speed of adjustment varies with the 
extent of deviation from the LOP.  
 
Wheat is one of the most important grains and is produced and consumed widely 
across the world. The major wheat exporting countries are the U.S., Canada, EU, 
Australia and Argentina, and together account for approximately 90% of the total 
wheat traded (Ghoshray 2002). Among individual countries price differences arise 
principally because of factors such as transportation costs and quality differences. 
Differences in environment and genetics among wheat producing areas of the world 
  3or within one country result in wide variations in the characteristics of wheat 
produced. The U.S. alone exports three classes of wheat in significant amounts; these 
being the Hard Red Winter (hereafter U.S. HRW), Soft Red Winter (hereafter U.S. 
SRW) and Dark Northern Spring (hereafter U.S. DNS). Australia predominantly 
exports a winter wheat, Australian Standard White, hereafter (ASW) which is very 
similar in quality and end use characteristics to the U.S. HRW wheat. Argentinean 
Trigo Pan wheat (hereafter ATP) competes with the U.S. HRW as it has similar end 
use characteristics. Australia and Argentina compete with the U.S. HRW wheat. The 
U.S. DNS competes with Canadian Western Red Spring (hereafter CWRS) wheat. In 
the case of spring wheat, the U.S. and Canada compete for the East Asian markets. 
The EU exports wheat which is considered as a soft winter wheat. The U.S. SRW 
wheat and the EU wheat compete for market share particularly in North African 
countries (Barassi and Ghoshray 2007).  
 
This note proposes an alternative novel framework for the empirical analysis of wheat 
export price relationships. The rationale for gradual rather than sudden regime shifts 
lies in the heterogeneous reaction of agents to changes in transactions costs, with each 
exporter responding differently especially to changes occurring in the proximity of the 
thresholds (Michael et al., 1997). Further, this study employs weekly data which 
reduces the aggregation bias found in studies that use monthly data (Taylor 2001). 
The following section describes the econometric model, followed by a discussion of 
the empirical results. The final section concludes. 
 
2. Econometric Model 
The most common expression of the LOP is given by the equation below: 
 
t t t z P P + + = 2 1 β α           ( 1 )  
 
where   and   are non-stationary I(1) prices in logs,  t P 1 t P2 α  is an arbitrary constant 
that accounts for transactions costs, β  measures the elasticity of price transmission 
and   is the error term which may be serially correlated. To test the LOP one may 
employ the standard Engle Granger test for cointegration of   and  . To illustrate 
t z
t P 1 t P 2
  4the method, (1) is estimated using OLS. The second step runs a Dickey-Fuller test on 
the estimated residuals of (1) of the following kind: 
 
1 tt zz t γ ω − Δ= +           ( 2 )  
 
where  t ω  is a white noise error term. If  t ω  is not white noise, an Augmented Dickey 
Fuller (ADF) test may be used where lagged values of  t z Δ  may be added to (2). 
Rejecting the null hypothesis   0 (: 0 H ) γ =  of no cointegration implies that the 
residuals of (1) are stationary.  
 
This note employs a test for cointegration allowing for nonlinear ESTAR adjustment 
to equilibrium designed by Kapetanios, Shin and Snell (2006), henceforth KSS. The 
test involves reformulating (2) to give the following nonlinear ESTAR process:  
 
( )
2
11 1e x p tt t zz z t γ θ −− ⎡⎤ Δ= − − +
⎣⎦
ε      ( )
2 ~i.i.d 0, t ε σ   (3) 
 
The null hypothesis of no cointegration for this test procedure is  0 : H 0 θ =  against 
the alternative  1: H 0 θ > . However, testing this null hypothesis directly is not 
feasible, since γ  is not identified under the null. Thus, KSS compute a Taylor series 
approximation to the ESTAR model under the null to obtain the following auxiliary 
regression: 
 
3
1 tt zz t δ ω − Δ= +           ( 4 )  
 
In the general case when the errors in (3) are serially correlated in a linear fashion 
then (1) may be extended to 
  
()
2
11
1
1e x p
p
ti t i t t
i
zz z z t β γθ −− −
=
⎡⎤ Δ= Δ + − − +
⎣⎦ ∑ ε   ( )
2 ~i.i.d 0, t ε σ   (5) 
 
and the auxiliary regression with  p augmentations is obtained to be: 
  5 
3
1
1
p
tt i t i
i
zz z t δ β −−
=
Δ= + Δ + ∑ ω
0
.          ( 6 )  
 
where the lagged values of   are included to correct for plausible serially correlated 
errors. To choose the number of lags we follow significance procedure proposed by 
KSS. In both cases the null hypothesis to be tested is 
t z Δ
0 : H δ =  against the alternative 
0 : 0 < δ H  using a   test. KSS show that the   test does not have an 
asymptotic standard normal distribution and undertake stochastic simulations to 
obtain the asymptotic critical values. 
NLEG tˆ NLEG tˆ
 
The existence of cointegration motivates the specification and estimation of the 
following nonlinear ESTAR–ECM model: 
 
t u t P t z t z t P + Δ + − ⎥ ⎦
⎤
⎢ ⎣
⎡ ⎟
⎠
⎞ ⎜
⎝
⎛
− − − = Δ 2 1
2
1 exp 1 1 β θ γ       ( 7 )  
 
where  is a possibly autocorrelated error term. In order to overcome the problem 
that the 
t u
γ  is not identified under the null, (7) is approximated using the Taylor series 
to obtain: 
 
t u t P z t P t + Δ + = Δ − 2   1
3
1 β δ          ( 8 )  
 
From (8) we compute the   statistic for the null of no cointegration, that is,  NLECM tˆ
0 : H 0 δ =  against the alternative of nonlinear ESTAR cointegration, that is, 
0 : 0 < δ H . As with the  , KSS undertake stochastic simulations to obtain the 
asymptotic critical values of  . KSS show using Monte Carlo simulations, that 
the two proposed tests,  and  have good size properties and superior 
power properties than the standard Engle Granger test. The simulations conducted by 
KSS show that the power gain is substantial, when 
NLEG tˆ
NLECM tˆ
NLEG tˆ NLECM tˆ
θ  is relatively small. They further 
  6demonstrate that the  is superior to the standard Engle-Granger and   
when the regressors are weakly endogenous in the cointegrating regression.  
NLECM tˆ NLEG tˆ
 
3. Empirical Results 
The data used for this analysis are weekly average export price quotations (FOB) 
from 9 September 2002 to 21 September 2007. The wheat prices used in this study 
include the ATP, ASW, U.S. HRW (Gulf port), U.S SRW (Gulf port), U.S. DNS 
(Gulf port), CWRS (St. Lawrence port) and EU Standard wheat. The data was 
obtained from the World Grain Statistics published by the International Grains 
Council. All prices are quoted in US dollars. The subsequent analysis of the data is 
carried out on the logarithm of prices.  
 
Figure 1 illustrates the wheat export prices used in this study. An interesting feature 
can be noticed from the data. The similar price patterns suggest that there is 
considerable opportunity for arbitrage among different classes of wheat. The 
similarity in price patterns is greater when considering the wheats’ which compete 
directly with each other for market share.  
 
[Figure 1 about here] 
 
The prices were initially tested for their order of integration. A battery of unit root 
tests were conducted to assess the appropriate order of integration of the variables. 
Besides the ADF tests, more powerful tests such as the GLS de-trended version of the 
standard Dickey Fuller (DF) test due to Elliot et. al., (1996) and the unit root test due 
Perron and Ng (1996) were employed. As a confirmatory test the KPSS test due to 
Kwiatkowski,  et. al., (1992) was conducted. All the unit root test results for the 
variables conclude that the prices are I(1). The results are not reported here for 
brevity.
2
 
We apply the Engle Granger (1987) methodology on four different price pairs 
following the long run equilibrium relationship given by equation (1). The pairs are 
chosen by regressing ATP and ASW export prices on the U.S. HRW wheat; U.S. 
                                                 
2 The results are available from the author on request. 
  7DNS on CWRS wheat; and U.S. SRW on EU wheat. These pairs are chosen carefully 
by establishing from the discussion in the earlier section as to which classes of U.S. 
wheat compete or are chosen as a reference price by other wheat exporters. The 
results of the test are shown in the second column of Table 1. The key point to note is 
that the Engle-Granger t-statistic is greater than the critical value in only one of the 
four possible pairs at the 10% significance level, that is, the [U.S.(DNS), CWRS] pair. 
This implies that for this pair, the null of no cointegration can be rejected, which 
implies that the two prices are cointegrated.  
 
[Table 1 about here] 
 
Using the linear method we find that the results are unfavorable to the LOP.   
However, a completely different conclusion emerges from the results of the   
test. In this case, except for the [CWRS,U.S.(DNS)] price pair, we are able to reject 
the null of no cointegration for all of the remaining three price pairs. However, when 
considering  , we find all the price pairs are cointegrated. Using Non-linear 
Least Squares, we obtain the estimates of   from the alternative ESTAR model. 
Given that 
NLEG tˆ
NLECM tˆ
θ ˆ
θ  is scale dependent, in order to facilitate convergence, we follow KSS by 
normalizing the  series to have a unit sample variance. The results for   and the t-
statistic are given in Table 1. KSS acknowledge that although the t-statistic in this 
case cannot be employed to test for significance from zero, the estimate of 
t z θ ˆ
θ  can be 
considered “significant” if the asymptotic 95% confidence interval around the 
estimate excludes zero. Following KSS we find θ  “significant” in all cases. It can be 
concluded that the power of the   is substantial given the low value of   
which varies between 0.001 to 0.003. The finding demonstrates that the results 
obtained from linear and nonlinear tests can be drastically different. 
NLECM tˆ θ ˆ
 
4. Conclusion 
This note employs a novel method to determine whether the export prices of wheat 
are integrated. The results conclude that all the prices cointegrate in pairs, implying 
that the international wheat market is highly integrated. This result is obtained by 
testing for cointegration using a non-linear ESTAR–ECM approach which has good 
  8size properties and superior power properties than the standard Engle Granger test. 
The results further suggest that owing to transactions costs, it is quite plausible that 
the further the prices deviate from each other, the larger will be the arbitrage that will 
drive the prices close to each other. However, arbitrage will be limited as the various 
wheat prices employed in this study may be linked to highly variable transactions 
costs or some other form of imperfect competition. 
 
 
  9References 
Barassi, M.R. and A. Ghoshray (2007) “Structural Change and Long Run 
relationships between US and EU Wheat Export Prices” Journal of Agricultural 
Economics, Vol. 58, p.76 – 90. 
 
Balcombe, K. Bailey, A. and J. Brooks (2007) “Threshold Effects in price 
Transmission: The Case of Brazilian Wheat, Maize and Soya Prices” American 
Journal of Agricultural Economics, 89, 308 – 323.  
 
Baulch, B. (1997) “Transfer Costs, Spatial Arbitrage and Testing for Food Market 
Integration” American Journal of Agricultural Economics, 9, 477 – 487.  
 
Binkley, J.K., and B. Harrer (1981) “Major Determinants of Ocean Freight Rates for 
Grains: An Econometric Analysis” American Journal of Agricultural Economics, 63, 
47 – 54. 
 
Elliot, G., Rothenberg, T.J. and Stock, J.H. (1996) “Efficient Tests for an 
Autoregressive Unit Root” Econometrica, Vol. 64, p. 813–836.  
 
Engle, R.F. and C.W.J Granger (1987) “Cointegration and Error Correction: 
Representation, Estimation and Testing” Econometrica (49), 251 – 276. 
 
Ghoshray, A. (2002) “Asymmetric price Adjustment and the World Wheat Market” 
Journal of Agricultural Economics, Vol. 53, p.299 – 317.  
 
Kapetanios, G., Shin, Y. and Snell, A. (2006). “Testing For Cointegration In 
Nonlinear Smooth Transition Error Correction Models,” Econometric Theory, Vol. 
22, No. 2, p. 279–303.  
 
Kwiatkowski, D., Phillips, P.C.B., Schmidt, P. and Shin, Y. (1992) “Testing the Null 
Hypothesis of Stationarity against the Alternative of a Unit Root” Journal of 
Econometrics, Vol. 54, p. 159–178.  
 
  10Michael, P., Panos, A., Peel, D. (1997). Transactions Costs and Nonlinear Adjustment 
in Real Exchange Rates: An Empirical Investigation. Journal of Political Economy 
105, 862 – 879.  
 
Perron, P. and Ng, S. (1996) “Useful Modifications to some Unit Root Tests with 
Dependent Errors and their Local Asymptotic Properties” Review of Economic 
Studies, Vol. 63, p. 435–465.  
 
Taylor, A.M. (2001) “Potential Pitfalls for the Purchasing Power Parity Puzzle? 
Sampling and Secification Biases in mean reversion Tests of the Law of One Price” 
Econometrica, Vol. 69, p. 473 – 498. 
  11 
Table 1:  Cointegration Tests and Estimates for the ESTAR parameter 
  EG tˆ   NLEG tˆ   NLECM tˆ   θ ˆ  θ tˆ  
ATP=    [] (HRW)   U.S. f –2.31 –3.37**    –3.05*  0.002 2.94 
ASW=   [] (HRW)   U.S. f –2.57   –4.10***  –5.13*** 0.003  11.94 
CWRS=    [] (DNS)   U.S. f –3.33* –2.90    –3.64**  0.001  4.13 
EU=   [ (SRW)   U.S. f ] –2.43   –4.01***  –4.15*** 0.002  5.06 
***, **, and * denote significance at the 1% level, 5% level and 10% level respectively. Following 
Kapetanios et. al. (2006) the lag lengths for the cointegration tests are chosen using the general to 
specific method. 
  12Figure 1: Wheat Export Prices
U.S./ton
Argentina
2002 2003 2004 2005 2006 2007
100
150
200
250
300
350
Australia
2002 2003 2004 2005 2006 2007
150
200
250
300
350
U.S. HRW
2002 2003 2004 2005 2006 2007
100
150
200
250
300
350
400
U.S. SRW
2002 2003 2004 2005 2006 2007
100
150
200
250
300
350
U.S. DNS
2002 2003 2004 2005 2006 2007
150
200
250
300
350
Canada
2002 2003 2004 2005 2006 2007
150
200
250
300
350
EU
2002 2003 2004 2005 2006 2007
125
175
225
275
325
 
 
 
 
  13

Nonlinear Price Transmission in Wheat Export Prices

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