Stepwise model selection criteria were tested against the restrictive forms to determine the appropriate model and to confirm the law of one price for the US soybeans. Analysis shows less than one international price transmission and exchange rate elasticities in the long run indicate an incomplete exchange rate pass through.International Relations/Trade,

Adhikari, Murali

Houston, Jack E.

Kinnucan, Henry W.

Paudel, Laxmi

English

Research Papers in Economics

 
 
 
 
An Analysis of International Price and Exchange Rate Elasticity for US Soybeans: The 
Case of Japan 
 
 
 
Laxmi Paudel 
Graduate Student 
Dept of Agricultural and Applied Economics 
The University of Georgia, Conner, 205 
Athens, GA 30602 
email:lpaudel@agecon.uga.edu 
 
Dr. Henry W. Kinnucan 
Professor 
Dept of Agricultural economics and Rural Sociology 
Auburn University, Comer, 213 
Auburn, AL 36849 
email:hkinnuca@acesag.auburn.edu 
 
Murali Adhikari 
Graduate Student 
Dept of Agricultural and Applied Economics 
The University of Georgia, Conner, 205 
Athens, GA 
email: madhikari@agecon.uga.edu 
 
 
 Dr. Jack E. Houston 
 Professor 
Dept of Agricultural and Applied Economics 
The University of Georgia, Conner, 305 
Athens, GA 
email:jhouston@agecon.uga.edu 
 
 
Selected Paper prepared for presentation at the Southern Agricultural Economics Association 
Annual Tulsa, Oklahoma, February 18, 2004  
 
 
 
 
 
 
 
 
Copyright 2004 by [authors].  All rights reserved.  Readers may make verbatim copies of this 
document for non-commercial purposes by any means, provided that this copyright notice 
appears on all such copies.  
 
1 
 
 
An Analysis of International Price and Exchange Rate Elasticity for US Soybeans: The 
Case of Japan 
 
Abstract 
Stepwise model selection criteria were tested against the restrictive forms to determine the 
appropriate model and to confirm the law of one price for the US soybeans. Analysis shows less 
than one international price transmission and exchange rate elasticities in the long run indicate an 
incomplete exchange rate pass through. 
Key words: Exchange rate, Law of one price, model selection, and Price transmission 
 
With the export of more than half of the world’s soybeans and soybean products, the United 
States is one of the leading soybean exporters of the world (American Soybean Association).  
Before 1974, the United States (US) had dominant position in the international soybeans market.  
However, the emergence of other competitor countries mainly due to the growing strength of the 
US dollars threatened the market position of US soybeans in recent years. Price transmission 
elasticity and exchange rate elasticity define the mechanism of international export market and 
changing market positions of exporting countries.  The relationship between international prices 
and the domestic prices, which brings internal adjustment in supply and demand, is crucial to 
define the responses of importers and exporters to international price changes.   
 
In spite of the significant role of price transmission and exchange rate elasticity in international 
export markets, There exist conflicting views among the marketing researchers about the 
magnitude of price transmission and exchange rate elasticities.  The study results of Bredahl,  
 
2 
Myers, and Collins (1979) suggest zero and one values for the price transmission elasticity.  
Johnson (1977) assumes perfect price transmission, and Pick and Carter (1994) indicate less than 
one exchange rate pass through. 
   
The law of one price maintains that the foreign and domestic prices of a commodity will be equal 
when both are expressed in the same currency unit net of transportation costs (Goodwin, 
Grennes, and Wohlgenant, 1990).  The purpose of this research is to confirm whether 
international price transmission elasticities for US soybeans confirm the law of one price (LOP).  
The freight rates and their volatility impact international soybeans price and omission of 
transportation costs while examining the price linkage could lead to a specification error. 
Therefore, we include transportation cost in our analysis. 
 
Model Specification  
For the estimation of exchange rate and price transmission elasticities, a simple mark up model 
was developed: 
Pi = (pd + ti) Zi           --------------------(1)                                                                                  
where i indexes the export market, Pi is the foreign market price of soybeans expressed in the 
foreign currency (FCU), pd is the domestic farm price of soybeans expressed in domestic 
currency (US dollar), ti is the transportation cost expressed in domestic currency (US dollar), and 
Zi is the bilateral exchange rate (FCU/ US dollar). Taking the total differential of (1):  
  ∆Pi = Zi ∆pd + pd ∆Zi + ∆Ti  ………………………………………………..(2) 
Where Ti = ti Zi is the transportation cost expressed in foreign currency units (FCU). Dividing 
the above equation by Pi, and noting that Pi = piZi where pi is the export price expressed in  
 
3 
domestic currency (US dollars), yields: 
∆Pi/ Pi = (pd/ pi)  ∆pd/ pd + (pd/ pi) ∆Zi/ Zi + (ti/ pi) ∆Ti/ Ti  ………………. . (3)               
which can be written in a simpler notation as 
Pi
*
 = ψi pd* + ζi Zi* + δi Ti* ……………………………………………….(4)                                                          
Where asterisked variables indicated relative changes (e.g., Pi
* = ∆Pi/ Pi ) and ψi = ζi < 1)  that is, 
equation (1) implies that the price transmission and exchange rate elasticities are equal and less 
than one.  Similarly, (1) introduces a restriction on the transportation cost, ψi = (1- δi).  Namely, 
the transportation cost elasticity equals one minus the price transmission elasticity, which implies 
ψi + δi = 1. 
 
In order to analyze the issue, we adopted a modeling philosophy suggested by Hendry (1995).  A 
general to specific modeling methodology was adopted to select the consistent model (Tomek 
and Kaiser, 1999).  Specifically, seasonality, trend, and inflation are included along with 
transportation cost in the price transmission model, since these variables have been found in the 
literature to be potentially important. Based on the outcome of seasonality, trend, and inflation 
tests, increasingly restricted models were tested to determine the lag structure. A double log 
model and 2SLS procedure taking the US price as endogenous variable were used to estimate the 
price transmission elasticity, transportation cost elasticity, and exchange rate elasticity.  The 
stepwise model selection criteria were to follow the modeling philosophy of Hendry. The general 
price linkage equation was specified as follows.   
 
4 
Model 1 
lnPt =  β0 + ∑
=
11
1 i
 βiDi + β12 lnPt-1 + β13 lnP t-2 + β14 lnPus + β15 lnPus t-1 + β16 ln Pus t-2 + β17 lnEx + 
β18 ln Ext-1+ β 19 ln Ex t-2 + β 20 ln Tn + β 21 ln inf + β22 Time + εt 
Where  
β0 = intercept  
Di = Seasonality variables where i = 1…………. 11; 
Pt = Export price of soybeans; 
Pt-1 = Export price of soybeans expressed in FCU in one period lag; 
Pt-2 = Export price of soybeans expressed in FCU in two period lag; 
Pus = US farm price of soybeans expressed in dollar per ton; 
Pus t-1 = US farm price of soybeans expressed in dollar per ton in one period lag; 
Pus t-2 = US price of soybeans expressed in dollar per ton in two period lag; 
Ex = Exchange rate expressed in unit of domestic currency;  
Ext-1 = Exchange rate expressed in FCU in one period lag;  
Ex t-2 = Exchange rate expressed in FCU in two period lag;  
Tn =Transportation cost of soybeans expressed in FCU per ton; 
Inf = Inflation rate of the different export countries; 
Time = Trend variable;  
 
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εt = a white noise error term in the model; 
 
The sign of price, transportation cost, and exchange rate are expected to be positive.  The foreign 
price, domestic price, and exchange rate were specified with two lags (Ravalion, 1986). Given 
the monthly data, two lag models were considered sufficient to reflect a plausible lag structure.  
In order to minimize multicolinearity problem, lags of inflation and transportation cost were 
ignored. Initially, eleven dummy variables were included in the model to capture the seasonal 
variations in export markets.  The exchange rate and export prices were included in the model to 
account for the inflation rate. 
Model 2 
 
 lnPt =  β0 + βiDi + β12 lnPt-1 + β15 lnPus t-1 + β16 ln Pus t-2 + β17 lnEx + β18 ln Ext-1+ β 19 ln Ex t-2 + εt 
 
After selecting the most appropriate model for Japanese export market, hypothesis testing for 
exchange rate elasticity and price transmission elasticity were carried out as:  
H0: β16 = β18 
H1: H0 not true. 
Data 
In order to find out the price transmission elasticity and exchange rate elasticity, the monthly 
time series data from January 1995 to December 2002 were collected from different sources.  
The soybean transportation rate data is obtained from Heigh and Hazzle of Texas A& M 
University and USDA. The monthly exchange rate was gathered from Pacific Commerce.   
 
6 
The US farm price was collected from the National Agricultural Statistics Service (NASS).  
The soybean export price of Japan was gathered from the Foreign Agricultural Service (FAS).  
Except exchange rates, remaining data were in the nominal terms.  The export price, exchange 
rate, and transportation cost data were expressed in Japanese yen while the US farm price was 
expressed in US dollars.  The Japan CPI information was gathered from the official web pages of 
central bank of Japan. The inflation rate was calculated by dividing the Japan’s CPI by the US 
CPI.  
Results and Discussions 
The step wise analysis using SAS statistical package shows the significant effect of 
exchange rate (first and second lag), US price (first and second lag), and seasonal effects of 
January, February, May, and August. Analysis reveals no significant effects of 
transportation cost, inflation, US price, and time. As the impacts of transportation cost was 
statistically insignificant, we select the model 2 as the best model. 
 
Due to the use of double log functional form, the estimated coefficients represent the 
estimated elasticities of corresponding variables.  The estimated coefficient of the lagged 
dependent variable was significant and between zero and one as required to satisfy a stable 
condition. The model has high R
2 and adjusted R
2 values showing the validity of the model.  
Plotting of residual versus predicted value to test the heteroscedasticity shows no such a 
pattern (figure 1). The DW test indicates no autocorrelation problem (Figure 2).  
The estimated coefficients of the model (Table 1) are short run elasticities.  The estimated 
international price transmission elasticities (first lag and second lag) and the exchange rate  
 
7 
elasticities (base, first, and second lag) of Japan were (0.18, 0.33) and (0.46, 0.61, and –0.46) 
respectively and were statistically significant.  
 
Table 1.  Estimate of Parameter in Japan Export Market Using Model Selection Criteria 
Variables Estimate  Error  T-value  P-value 
Intercept  1.32        0.206  6.43  0.0001 
PJt-1 0.33 0.085  3.87 0.0003 
PUSt-1 0.18  0.086  2.10  0.0402 
PUSt-2 0.33  0.118  2.99  0.0041 
EX 0.46  0.114  4.02  0.0002 
Ext-1 0.61 0.190  3.21 0.0022 
Ext-2 -0.46  0.118  -3.86  0.0003 
D1  0.039 0.013 3.07  0.0032 
D2  0.035 0.013 2.62  0.0112 
D5  0.025 0.011 2.12  0.0386 
D8 -0.023  0.012  -1.93  0.0587 
F- Value  407.72 
(<0.0001) 
   
RMSE 0.02     
R
2 0.98     
ADJ R
2 0.98     
Note: (t-1) and (t-2) indicates the lag structure of that variable in the model 
The long run elasticities were calculated by dividing the short run elasticities by one minus the 
estimated coefficients of the lagged dependent variables.  Long run and short run elasticities  
 
8 
are presented in Table 2. The estimated long run elasticities of US farm price and exchange 
rates were (0.27, 0.49) and (0.69, 0.91, and –0.69) respectively. It reflects an unequal effect of 
farm price and exchange rate changes in the Japanese market.  Study results reveal that the law 
of one price does not exist in Japanese market. 
 
Table 2. Estimates of Long Run and Short Run Elasticities in the Japanese Export Market: 
 
Variables  SR Elasticity  LR Elasticity 
PUSt-1 0.18  0.27 
PUSt-2 0.33  0.49 
LEX 0.46  0.69 
LEXt-1 0.61  0.91 
LEXt-2 -0.46  -0.69 
Note: (t-1) and (t-2) indicates the lag structure of that variable in the model 
                              
 
The significant lagged dependent variables suggest a time lag to adjust the changes in exchange 
rate and the US price. By using the adjustment formula, {(coefficient of lagged dependent 
var)
N=0.01}, it takes about 4.15 months to respond fully to a permanent change in the US farm 
price and bilateral exchange rate.  If the estimated coefficient of the lagged dependent variable 
was not significant, soybean price in Japan would respond instantaneously to changes in the US 
soybean farm price, and exchange rates resulting in to a well integrated and efficient market 
mechanism. 
 
  
 
9 
In the long run, the exchange rate change had stronger effects on soybean export price than 
change in US farm prices.  The estimated coefficient of exchange rate was closure to unity in the 
first lag suggesting an almost complete exchange rate pass through in the Japanese market. It 
means an 1% change in the US-foreign currency rate results in a less than 1% change in the 
foreign price given the sufficient time for markets to adjust.  
 
In order to test the law of one price, we tested a hypothesis, which suggests an equal price 
transmission elasticity and exchange rate elasticity in the long run. The test results of the above 
hypothesis tests are presented in Table 3. The elasticity of the transportation cost was not 
significant in Japan rejecting the law of one price. Rejection of LOP might have resulted from 
the market interventions which are not explicitly modeled in our study, an issue worthy of further 
study.  
Table 3.  Hypothesis Test 
Probability level  Countries Calculated 
F test
a 
Calculated 
F test
b 
Critical 
F test
c  a b 
Japan 16.90  7.22  3.96  0.0001 0.0091 
a the hypothesis of exchange rate elasticity is equal to the transmission price elasticity. 
C Critical values are expressed in 0.05% level 
Based on the number of significant variables, the model has performed well in defining the price 
transmission and exchange rate elasticities. The estimated coefficients of the US farm price had 
the correct signs and were significant at the 1% probability level. The study results suggest 
significant impacts of changes in the US farm prices and bilateral exchange rates on Soybeans 
export price.  In the long run, the exchange rate had stronger effect on export price than change 
in US farm prices.     
 
10 
Figure1. Test of Homoscedasticity in the US Soybean export market: Japan 
   Figure 2: Test of 
Autocorrelation in the US Soybean export market: Japan 
  
 
11 
Conclusions 
  Information regarding exchange rate and transmission price elasticities is crucial for 
policy purposes. In this analysis, the stepwise model selection criteria were used to choose the 
consistent model. The elasticities were estimated by using 2SLS procedures. Out of other major 
US trading partners, Japan was selected for the study purpose as Japan represents the major US 
soybeans exporting country.  The econometric analysis suggests that international price 
transmission elasticities and exchange rate elasticities for soybeans are less than one in both the 
short and the long runs. 
  
Exchange rate elasticity tends toward unity but not to exact unity in the long run, which suggests 
an incomplete exchange rate pass through, i.e., a 1% change in the US foreign currency results in 
a less than 1% change in the foreign price.  In our analysis, the transportation cost was not 
significant which suggests that omission of transportation cost does not significantly affect the 
results. Study results also show that the law of one-price does not hold in the Japanese market. 
Rejection of LOP in Japanese market might be due to market interventions which is not 
explicitly modeled in our study.  
 
References  
 American Soybean Association.  Several issues published from the website of 
http://www.amsoy.org 
Bolling, Christine.  “Price and Exchange Rate Transmission Revisited: The Latin America 
Case.” Elasticities in International Agricultural Trade Ed C.A.Carter and W.H Gardiner  
 
12 
Westview Press, Boulder and London.(1988). 
Bredahl, M E., W. H. Meyers, and K. J. Collins.  “The Elasticity of Foreign Demand for U.S. 
Agricultural Products: The Importance of the Price Transmission Elasticity.” Amer. J. 
Agr. Econ. 61(1979): 249-57. 
Collins, C.H.  “Price and Exchange Rate Transmission.” Agricultural Economics Research, 
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Collins, K., W. Meyers and M. Bredahl.  “Multiple Exchange Rate Changes and U.S. 
Agricultural Commodity Prices.” Amer. J. Agr. Econ. 63(1981): 32-46. 
Goodwin, B.K., Grennes, T., Wohlgenent, M. K.  “Testing the Law of One Price When Trade 
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Heigh, M.S., and H.L. Bryant. “The Effect of Barge and Ocean Freight Price Volatility in 
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Pick, D. H. and C.A. Carter.  “Pricing to Market with transactions Denominated in a Common 
Currency.” Amer. J. Agr. Econ. 76(1994):55-60. 
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Association. Several issues published from the website of http://www.amsoy.org Bolling, Christine. “Price and Exchange Rate Transmission Revisited: The Latin America Case.” Elasticities

Multiple Exchange Rate Changes and U.S.

Price and Exchange Rate Transmission.”

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Testing the Law of One Price When Trade Takes Time.”

The Effect of Barge and Ocean Freight Price Volatility

AN ANALYSIS OF INTERNATIONAL PRICE AND EXCHANGE RATE ELASTICITY FOR US SOYBEANS: THE CASE OF JAPAN

AN ANALYSIS OF INTERNATIONAL PRICE AND EXCHANGE RATE ELASTICITY FOR US SOYBEANS: THE CASE OF JAPAN

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