Asymmetric transmission
between terminal and
shipping point prices for
selected fruits
Byeong-Il Ahn* and Hyunok Lee**
June 2012
*Department of Food and Resource Economics
Korea University
Anam-dong Seongbuk-gu, Seoul, 136-701
South Korea
and
**Department of Agricultural and Resource Economics
University of California, Davis
Davis, CA 95616
This research was funded in part by California Department of Food &
Agriculture (CDFA) Specialty Crop Block Grant CFDA #10.170
1
Asymmetric transmission between terminal and shipping point
prices for selected fruits
Price transmission has drawn widespread interest from economists. Previous studies
analyzed price relationships in both input and output markets, among different links along the
supply chain, and across nodes in spatially disperse markets. A variety of products—from
agricultural commodities to petroleum products—has been the subject of empirical work.
One common assumption used in studies of price transmission is symmetry of responses to
shocks. That is, the magnitude of price transmission across markets or nodes does not
depend on the direction (up or down) of the initial price shock (Wohlgenant, 2001). A few
studies applied to agricultural commodities have attempted to investigate empirically this
assumption using a more general framework that separates the regimes by the direction of
initial price shock and allows the possibility of non-symmetric transmission (Karrenbrock,
1991; Azzam, 1999; Meyer and von Cramon-Taubadel, 2004; Kaufmann, 2005; Ahn and
Kim, 2008). Following this line of literature, commonly referred to as asymmetric price
transmission, the present study adds to the price transmission literature on specialty crops by
investigating the structure of price transmission in the context of the vertical market chain for
fruit markets in the United States. Focusing on the initial shipping point and terminal
(wholesale) links in the marketing chain, we examine short-term as well as cumulative price
responses of terminal prices to changes in shipping point prices.
In addition to providing empirical evidence related to asymmetry, previous studies on
asymmetric price transmission explored its interpretations. If the markets were efficient (and
some additional conditions are met), a price shock in one market affects the price of the
related market in a symmetric fashion. This suggests that the test of asymmetry could be
used to investigate market efficiency, and that the evidence of asymmetry would be
consistent with a market with asymmetric transaction costs, market power or some other
deviation from perfect competition (Meyer and von Cramon-Taubadel, 2004; Carmen and
Sexton, 2005; Koutroumanidis et al., 2009).
2
A number of studies of agricultural commodities suggested that the main driver of
asymmetric price transmission in a vertical marketing chain is market power (McCorriston
et al., 1998; Azzam and Schroeter, 1995; Chen and Lent, 1992; Bunte and Peerlings, 2003;
Carmen and Sexton, 2005). A party with market power can influence the price to increase
profits. Under such a situation, market participants with market power exploit the situation
differentially depending on the direction of the initial price shock.
We explore the implications of our test results for the underlying market structure of
marketing chains considered in this study. Of course, evidence of asymmetry does not
necessarily imply market power. Carlton (1989) suggests that unless the change in marginal
cost (the procuring price from the upstream marketing chain) is sufficiently large, retailers do
not implement a price change due to a menu or re-pricing cost. Bettendorf and Verboven
(2000) supported this claim empirically in the context of vertical markets for coffee. Other
explanations include Ball and Mankiw (1994) who focused on asymmetric adjustment of
nominal prices during the time of inflation, and Reagan and Weitzman (1982) who showed
how competitive industries result in asymmetric price transmission through their inventory
holding behavior. Finally, Bailey and Brorsen (1989) pointed out that asymmetric (or
imperfect) information about costs may cause asymmetric price transmission.1
We formally test the asymmetry of price transmission between the shipping point and
terminal prices using weekly price data spanning from 1998 to 2011. The model separates
the two regimes of the initial price shock and incorporates time lags of both explanatory and
dependent variables, which enables us to investigate the price adjustment process between
prices in different stages of the marketing chain. The empirical models are discussed in the
next section. Data description and preliminary tests on data and model specification,
including the tests on lag order, unit-root, causality and cointegration follow. We then report
the model estimation results, and conclude the paper with a summary and implications.
1
For more discussion, see Peltzman (2000) who investigated various plausible causes for price asymmetries, such as market
concentration, inventories, inflation-related asymmetric "menu costs" of price changes, or the fragmentation of the marketing
chain. His study supports none of these causes, except for the level of fragmentation of the marketing chain.
3
Empirical Model
The salient features of the models used in testing asymmetric price transmission involve the
segmentation of the regimes, differentiated by the sign of the initial price shock. Early
studies adopting regime segmentation include Wolffram (1971) and Houck (1977).2
Allowing the possibility of non-instantaneous price adjustments, Ward (1982) and Boyd and
Brorsen (1988) extended Houck’s model by incorporating lagged explanatory variables in the
vertical marketing chains of fresh vegetables and pork in the United States.3 The length of
lags in this framework corresponds to the duration of the price adjustment, and the
coefficients on the lagged explanatory variables indicate the magnitude of their impacts on
the dependent variable.
The main drawback of this approach relates to the time series properties of the data.
Recognizing that this simple approach is not consistent with common time series properties
of the data, Borenstein et al. (1997) and von Cramon-Taubadel (1998) applied a cointegration
method to the tests of asymmetric transmission between the crude oil and retail gasoline
prices and between producer and wholesale prices in the German pork market, respectively.
As a more comprehensive time-series approach, Krivonos (2004) adopted an error correction
model and characterized the long-run equilibrium price transmission in the world versus
producing-county coffee markets.
Developing the empirical model starts with defining the relationship between the current and
lagged prices in a marketing chain simply composed of the downstream and upstream
d
markets. Let Pt , denoting the downstream price at time t, depend on its own lagged values
u
and the contemporaneous and lagged upstream prices, P . Then, a typical autoregressive
distributed lag (ADL) model with the lag length of n can be specified as:
n
n
Pt  a0   a P   bi Pt ui   t . This equation assumes a symmetric relationship
d
i 1
d
i t i
i 0
2
Even though the typical asymmetric specification originates from Wolffram and Houck, the basic conceptualization of
asymmetric price transmission goes back to Farrell (1952), who first investigated empirically the irreversibility behavior of
the demand function of habitual consumption goods.
3 Houck’s (1977) model was developed to test the asymmetry in supply response in the U.S. milk and pinto beans markets
by extending the basic model concept by Wolffram (1971), who segmented the initial price shock into increasing and
decreasing phases.
4
between the changes in explanatory variables and the dependent variable. This symmetric
relationship is more immediate when the equation is expressed in differences,
n1
n1
Pt   ai P  bi Pt ui , where ∆ signifies a change from the value of the previous
d
i 1
d
t i
i 0
period. To incorporate the possibility of asymmetric transmission, we need to separate the
explanatory variables depending on the direction of the change, which can be specified using




binary variables, Ai Ai Bi and Bi :
(Model 1)
1 if
Ai  
0
n1
n1
n1
n1
i 1
i 1
i 0
i 0
Pt d     ai  Ai Pt di  ai  Ai Pt di  bi  Bi Pt ui   bi  Bi Pt ui  et
1 if Pt d i  0  1 if Pt ui  0
1 if Pt ui  0
, Ai  
, Bi  
Bi  
otherwise
otherwise
otherwise
otherwise
0
0
0
Pt d i  0
Equation (1) allows two types of asymmetric price transmission tests. First, we can test for
u
u
short-term asymmetric price transmission between Pt i and Pt d . If Pt i were


symmetrically transmitted to Pt d , estimated coefficients bi and bi would be the same.
Thus, asymmetric price transmission exists with respect to the ith lagged upstream price if two
coefficients are significantly different from one another. The second test is for cumulative
n 1
asymmetric price transmission. If the influences of
 B P
i 0

i
u
t i
n 1
dependent variable are symmetric, the cumulated coefficients
b
i 0

i
 B P
i 0
b
i 0
n 1
n 1
and

i

i
u
t i
on the
would be the same as
. Thus, the hypothesis of symmetric cumulative price transmission would be rejected
if these sums were significantly different from one another. The short-term symmetry
implies cumulative symmetry, but not vice versa. Further, the short-term asymmetry does not
imply cumulative asymmetry. Similar tests between the contemporaneous and lagged
dependent variables apply. That is, the short-term price adjustment is said to be asymmetric
if the data reject H 0 : ai  ai and the cumulative price adjustment is asymmetric if the data
5
reject H 0 :
n 1
n 1
i 1
i 1
 ai   ai .
Note that tests on asymmetric price transmission provide information about market efficiency
(or inefficiency) and market inefficiency is indicated by the asymmetry on the b coefficients.
n 1
Further, asymmetry confirmed with further statistical evidence of
b
i 1
n 1
greater than
b
i 1

i

i
being significantly
is termed positive asymmetry, which is consistent with the fact that
higher profits are earned by downstream participants than what they could have earned under
the efficient market (Carman and Sexton, 2005).
Another alternative model specification relates to the time series nature of the price variables.
Although equation (1) can capture the cumulative effects in price transmission, these models
essentially do not consider the effects of price transmission when price variables deviate from
d
u
their long run path. In general, differenced variables (such as Pt d , Pt i and Pt i ) tend
to be stationary, however, the original price variables may meander without showing the
constant mean or variance over time. Although the prices are not stationary, if a linear
relationship between these price variables is stable and the residual from this linear
relationship is white-noisy, we say that cointegration exists between these variables (Anders,
1995). If the existence of cointegration is identified, the asymmetric price transmission
model can be extended to specify the long-run adjustments by introducing the errorcorrection terms, as in von Cramon-Taubadel and Loy (1996). Given the error correction
model can be extended based on the results of the cointegration test, the presentation of the
error correction model will be deferred until we perform the cointegration test.
Data
One distinct characteristic of fresh fruits is perishability, which surely contributes to shortterm fluctuation of market prices. This implies that price transmission can be relatively in
short term and the data used to examine price transmission necessarily have to reflect such
6
short terms. In light of this, we searched for time series price data with short intervals.
The Marketing Service at the U.S. Department of Agriculture provides weekly prices of
major agricultural commodities at various marketing channels. We have chosen fresh
strawberries, apples, table grapes and fresh peaches as representative fruits, and for each of
these fruits, we collected weekly prices at the shipping point and terminal market. In terms
of selecting the location of the shipping point and terminal market, we picked the shipping
point in the region that is associated with the largest production and the terminal market that
likely handles the largest volume. Obviously, the terminal prices and shipping point prices
correspond to the upstream price and downstream price in our model, respectively. While
our data period spans from 1998 to 2011, depending on its season, the data series for each
fruit begins and ends in different months. Data details are provided in the appendix.
These two price series tend to move together, and fluctuate considerably over the time period
investigated. Price fluctuations are larger in the second half of the period for both series.
The time pattern of the price fluctuation suggests the possibility of non-stationarity of price
series, which violates the time series property of constant mean and variance. The comovement of these series further suggests the possibility of cointegration, as is often
manifested by the parallel pattern of non-stationary variables. The time series properties of
the data will be formally investigated next.
Preliminary tests
In this section we first consider the choice of lag orders and causality and then investigate
time series properties of the data. We select appropriate lag orders based on statistical
criteria, and perform the causality tests to identify the relationship between shipping point
and terminal prices. We conduct unit root tests on the variables used in empirical equations
to avoid spurious regression and erroneous interpretation of estimated results. We also test
for cointegration between the wholesale and factory prices for the possibility of including
long-run relations of these time series vectors in the empirical estimation.
7
Lag order choice and causality tests
The following vector autoregressive (VAR) model is used to determine the lag orders and
conduct the causality test:
 PtT   T   a1T b1T   PtT1   a2T b2T   PtT 2 
akT bkT   PtT k  etT 
 S    S    S S   S    S S   S   ...   S S   S    S 
 Pt     a1 b1   Pt 1   a2 b2   Pt  2 
 ak bk   Pt  k  et 
Within the VAR formulation expressed as above, the optimum lag order is selected using the
Akaike’s information criterion (AIC) and Schwartz Bayesian Information Criterion (SBIC).
We considered up to the fifth lag, and the lag order that produces the minimum information
criteria is selected (Anders, 1995). Table 1 presents the values obtained under the two
information criteria for each order of lags considered. Using these criteria, we selected the
lag order one for apples, lag order four for table grapes, lag order three for strawberries, and
lag order four for peaches.4
In specifying the empirical equations, our underlying assumption is that the current terminal
price is influenced by the shipping point prices, consistent with the usual assumption that
downstream prices are affected by upstream prices.5 However, this is not always the case,
and an easy example is the case of market power. Under the influence of market power, the
party with market power influences the price to his/her advantage and thus acts as an
initiating party in price causality. Thus, with no prior knowledge about the industry, we need
to empirically evaluate causality.
To check the causality between prices, we used the estimation results from the VAR model.
k
k
i 1
i 1
From the first equation of the VAR model ( Pt T   d   aid Pt Ti   bid Pt Si ), we can say that
4
Due to the space limitation, we do not present the full estimation results of the VAR model.
5
The opposite direction of causality is, of course, plausible as in Koutroumanidis et al., which deals with a market where
imports represent a large share of domestic consumption, and the import price leads the consumer price. They find that
under such market conditions, causality is from downstream to upstream markets, i.e., the consumer price affects the
producer price.
8
T
P S causes P if we reject the null hypothesis H0: b1d  b2d  ...  bkd  0 . Likewise, using
k
k
i 1
i 1
the results of the second equation of the VAR model ( Pt S   u   aiu Pt Ti  biu Pt Ti ), PT is
said to cause P S , if we reject the null hypothesis H0: a1u  a2u  ...  aku  0 . Table 2 shows
the causality test results. The test results show that except for strawberries, shipping point
prices cause terminal prices, which is consistent with the underlying assumption upon which
our model specification is based.6 However, for strawberries, the causality of both directions
is strongly rejected, implying that the direction of price causality is inconclusive. This
invalidates the specification of either VAR equation and any statistical results obtained from
our asymmetric regression cannot be valid.
Unit-root tests
Unit-root tests are essential in checking the spurious regression and the existence of
cointegration. For the regression to be statistically meaningful, all the variables in the
regression have to be stationary. Specification tests concerning equation (1) include spurious
regression. For each variable used in equation (1), we conduct a unit root test by adopting
the Augmented Dickey-Fuller (ADF) test. The ADF test with an intercept and trend is based
n
on the following form of regression: Yt   0   t t  Yt 1    j Yt  j  ut , where Y is the
i 1
variable that is subjected to the unit-root test. The null hypothesis for testing the unit root is
  0 . If the absolute value of the ADF test statistic is greater than the absolute value for the
critical point, the hypothesis of unit root is rejected. Test results are provided in the appendix.
The hypothesis of unit root is rejected at 1% significance for every variable tested, strongly
indicating little possibility of spurious relationships for regression equation (1).
The validity of an error correction model requires a cointegration test on time series Pu and Pd.
This test is conducted in two steps. The stationarity (or non-stationarity) properties of these
6 Note that the findings of causality may result from the omission of external variables which affect both factory and
wholesale prices. To check this possibility, we estimated the structural VAR (SVAR) by including price indices of recycled
timber and furniture as input and output prices that may affect the fiberboard market (note that retail prices of fiberboard
were not available). The estimation results obtained from the models including these exogenous variables also found that
that factory prices still Granger-cause the wholesale prices.
9
time series are inspected first, and upon the evidence of non-stationarity, a cointegration test
is performed. We first apply the augmented Dickey-Fuller (ADF) test to each of time series
Pu and Pd using the same regression form employed in the previous unit root tests.7 Based
on the estimated ADF test statistics for shipping point and terminal prices (Table 3), the null
hypotheses of unit root process is rejected for both variables, implying that both time series
variables are stationary. Having obtained the evidence of stationarity, we do not proceed
with the Engle-Granger cointegration test, which thus precludes in the context of modeling
the error correction model approach.
Estimation results of asymmetric price transmission
Table 4 reports the results obtained from estimating model (1). All coefficients except one
(which is statistically insignificant) related to shipping point prices are positive, while all
lagged own-price effects except those for apples are negative. Positive shipping point price
effects indicate that the terminal price moves together with shipping point prices both current
and lagged, meaning a rise (fall) in shipping point price induces an increase (reduction) in
terminal price. While this finding is consistent with our intuition, negative lagged own price
effects are interesting. Except in the case of apples, previous terminal prices affect the
current terminal price in the opposite direction. Combined with the findings on positive
shipping point price effects, the significance of negative lagged own price effects is that the
lagged own prices work as a dampening factor, even though positive shipping point price
effects may dominate.
We have found distinct patterns of lagged price effects for each fruit. The lagged price
effects we obtained do not conform to the usual expectation that prices effects taper down as
the order of lag increases. For apples, one period lagged shipping price effect associated
with a negative price change is much larger than the current price effect (0.08 vs. 0.34). For
peaches, the second lagged shipping point price has the largest price effects among all lags
for both positive and negative changes, and for own price effects, lagged price effects tend to
7
Recall that we test the non-stationarity of the differenced variables such as Pt d and D  Pt u to check the spurious
regression for models 1 and 2. For the test for cointegration, we have to check the non-stationarity (unit root) of the original
variables Pu and Pd.
10
get larger as the lag increases.
F-test statistics for asymmetry tests are reported in Table 4 and the summary interpretation of
the test results is provided in Table 5. The null hypothesis that the effect of the current
shipping point price is symmetrically transmitted to the current terminal price is rejected for
apples and peaches but not for table grapes. These asymmetry effects are, however, positive
for apples and negative for peaches, meaning that for apples the terminal price responds with
a larger margin to a shipping point price increase than to a decrease and the reverse is true for
peaches. Nevertheless, as indicated by the magnitude of the estimated coefficients for b0


and b0 , positive asymmetry for apples is substantial while the negative asymmetry for
peaches is relatively marginal. Asymmetry of cumulative FOB price effects is also positive
for apples, but inconclusive for peaches. For table grapes, the symmetry of the cumulative
effect of shipping point prices cannot be rejected. The hypothesis of symmetric cumulative
lagged own price effects is strongly rejected for apples but cannot be rejected for table grapes
and peaches.
We have also examined asymmetric price transmission in the context of quantile regression.
Quantile regression, which was introduced by Koenker and Bassett (1978), extends the
regression model to conditional quantiles of the response variable. Quantile regression is
useful when the rate of change in the conditional quantile, expressed by the regression
coefficients, depends on the quantile. In addition to the fact that the quantile regression
estimates are more robust against outliers in the response measurements, the quantile
regression approach produces a comprehensive analysis of the relationship between variables.
We considered the quantiles at the 20% increment, and summarized the asymmetry test in
Table 6.
A distinct pattern of asymmetry emerges from table 6. Negative asymmetry is, in general,
found mostly at low levels of quantiles and positive asymmetry mostly at high levels of
quantiles. That is, at a low level of price change the terminal price responds more to a decline
in the FOB price than to an increase. On the other hand, at a relatively larger price change,
the terminal price responds more to an increase in the FOB price than to a decrease. These
11
patterns are pronounced especially for apples and table grapes. In comparison with the mean
value estimation (under the usual least square estimation method), quantile estimations tend
to produce negative asymmetry associated with changes in FOB price results at a relatively
low quantile range. There may be a number of explanations for positive asymmetry at a high
quantile level. For instance, the profit-extracting behavior of terminal marketers would be a
possibility, which is allowed only under certain market conditions. Another possibility has to
do with the operating structure of terminal marketers. Suppose that a large increase in the
FOB price occurred after a serious supply shock. A contraction in supply causes a reduction
in total product quantities at the terminal market. It is easy to imagine that the terminal
market may operate in less than full capacity in this case. This likely increases per-unit
operating cost, which results in an increase in terminal price exceeding the increase in FOB
price. Regarding the negative asymmetry at a relatively low level of price change,
explanations are not immediate.
Conclusions
This article has developed and tested hypotheses of asymmetric price transmission in fruit
prices using the appropriate statistical tools and after tests to account for time series
properties of the data. The econometric results have found evidence of asymmetric price
movements between shipping point and terminal markets for fruits. We are not able to say
definitively what drives the asymmetry but provide some potential rationales and ideas for
further investigation.
12
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09/10/2005
12/31/2005
04/22/2006
08/12/2006
12/02/2006
3/24/2007
7/14/2007
11/3/2007
2/23/2008
6/14/2008
10/4/2008
1/24/2009
5/16/2009
9/5/2009
12/26/2009
4/17/2010
8/7/2010
11/27/2010
3/19/2011
7/9/2011
10/29/2011
Fig. 1.a-d. weekly prices ($/lb) for table grapes, fresh apples, fresh peaches, and fresh
strawberries at terminal market and shipping point (FOB)
Table grape terminal and FOB prices
3.5
3
2.5
2
1.5
1
0.5
Grape terminal prices ($/lb)
terminal apple prices
Grape FOB prices ($/lb)
Fresh apple terminal and FOB prices
1.2
1
0.8
0.6
0.4
0.2
0
FOB apple prices
15
01/10/1998
05/30/1998
10/17/1998
03/06/1999
07/24/1999
12/11/1999
04/29/2000
09/16/2000
02/03/2001
06/23/2001
11/10/2001
03/30/2002
08/17/2002
01/04/2003
05/24/2003
10/11/2003
02/28/2004
07/17/2004
12/04/2004
04/23/2005
09/10/2005
01/28/2006
06/17/2006
11/04/2006
3/24/2007
8/11/2007
12/29/2007
5/17/2008
10/4/2008
2/21/2009
7/11/2009
11/28/2009
4/17/2010
9/4/2010
1/22/2011
6/11/2011
10/29/2011
05/23/1998
10/03/1998
02/13/1999
06/26/1999
11/06/1999
03/18/2000
07/29/2000
12/09/2000
04/21/2001
09/01/2001
01/12/2002
05/25/2002
10/05/2002
02/15/2003
06/28/2003
11/08/2003
03/20/2004
07/31/2004
12/11/2004
04/23/2005
09/03/2005
01/14/2006
05/27/2006
10/07/2006
2/17/2007
6/30/2007
11/10/2007
3/22/2008
8/2/2008
12/13/2008
4/25/2009
9/5/2009
1/16/2010
5/29/2010
10/9/2010
2/19/2011
7/2/2011
11/12/2011
Fresh peach terminal and FOB prices
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
peach terminal prices
strawberry terminal prices
peach FOB prices
Fresh strawberry terminal and FOB prices
4
3.5
3
2.5
2
1.5
1
0.5
0
strawberry FOB prices
16
Table 1. Lag order choice
Apples
Table grapes
Strawberries
Peaches
Criteria
Lag1
Lag 2
Lag 3
Lag4
Lag 5
AIC
-10.2381
-10.2600
-10.2901
-10.3130
-10.4519
SBIC
-10.1991
-10.1947
-10.1983
-10.1945
-10.3064
AIC
-3.3526
-3.6092
-3.6886
-3.8060
-3.7008
SBIC
-3.2993
-3.5159
-3.5507
-3.6190
-3.4588
AIC
-1.9766
-2.1087
-2.1231
-2.1201
-2.1510
SBIC
-1.9339
-2.0360
-2.0189
-1.9831
-1.9801
AIC
-6.1912
-6.4914
-6.8734
-6.9510
-7.009
SBIC
-6.1230
-6.3708
-6.6944
-6.7072
-6.6920
Choices of lag order: Apples = 1, table grapes = 4, strawberries = 3, peaches = 4
17
Table 2. Granger Causality test results
Apples
chi2
test statistic
Pr.( | chi2 | >
critical value)1
d.f.
0.0026
0.9591
1
30.8340
0.0000
1
0.7550
0.9444
4
P ) → Terminal
bT  b2T  ...  bkT  0
PT
Price( ) (H0: 1
)
T
P
H1: Terminal price( ) → Shipping point
41.3703
0.0000
4
a1S  a2S  ...  akS  0 )
PS
H1: Shipping point Price( ) → Terminal
11.4412
0.0096
3
166.11
0.0000
3
1.1427
0.8874
1
102.2311
0.0000
1
Causality
T
H1: Terminal price( P ) → Shipping point
S
Price( P )
S
S
S
(H0: a1  a2  ...  ak  0 )
S
H1: Shipping point Price( P ) → Terminal
T
Price( P )
Table
grapes
T
T
T
(H0: b1  b2  ...  bk  0 )
T
P ) → Shipping point
a S  a2S  ...  akS  0 )
(H0: 1
H1: Terminal price(
Price(
PS )
S
H1: Shipping point Price(
Strawberries
Apple
Price(
PS )
(H0:
Price(
PT )
(H0:
b1T  b2T  ...  bkT  0
)
T
P ) → Shipping point
a S  a2S  ...  akS  0
(H0: 1
)
H1: Terminal price(
Price(
PS )
S
P ) → Terminal
b1T  b2T  ...  bkT  0
H1: Shipping point Price(
Price(
PT )
(H0:
)
1. If the probability that chi2 test statistic is greater than the critical value is less than 0.05, we
reject the null hypothesis (H0), and the alternative hypothesis (H1) is accepted.
18
Table 3. Unit root test results
Variable
ADF test statistic
99% critical value
PT
-4.0922
-3.9710
PS
-4.5792
-3.9711
PT
-8.1362
-3.9740
PS
-14.4843
-3.9751
PT
-6.2987
-3.9712
PS
-5.2867
-3.9727
PT
-16.0236
-3.9780
PS
-13.4687
-3.9799
Apples
Table grapes
Strawberries
Peaches
19
Table 4. Estimation results
Table
grapes
Apples
Coefficient
Regressor


b0
b1
Std. Error
Coefficient
estimate1)
Std. Error
Coefficient
estimate1)
Std. Error
0.0002
0.0009
0.0084
0.0080
0.0053
0.0054
0.0600
0.8324***
0.0702
0.2030
0.1291
0.0879
0.7168***
0.1841
0.2647**
0.1301

D Pt

D Pt S1 0.2015***
0.0689
0.2646***
0.0855
0.5035***
0.1395

DPt S1 0.3446***
0.0907
0.6088***
0.1488
0.7430***
0.1223

D Pt S2
0.2896***
0.0908
0.0651
0.1808

D Pt S2
-0.0032
0.1442
0.1068
0.1148
b0
b1
Coefficient
estimate1)
D Pt S 0.6677***

Peaches
b2
b2

S
0.0796
b3
D P
0.3751***
0.1001
0.0792
0.1856
b3
D Pt S3
0.1344
0.1231
0.3420***
0.0973
b4 
D Pt S4
0.0174
0.0904
0.1947
0.1880
b4 
D Pt S4
0.1490
0.1074
0.1925**
0.0788
S
t 3

D PtT1 0.0229
0.0433
-0.1128*
0.0650
-0.0433
0.1058

DPtT1
0.0758
-0.2913***
0.0769
-0.0371
0.0988

D PtT2
-0.2388***
0.0724
-0.1345
0.1218

DPtT2
-0.1027
0.0720
-0.1696**
0.0840
a3
D PtT3
-0.3485***
0.0826
-0.1446
0.1255
a3
DPtT3
-0.0003
0.0611
-0.1666**
0.0756
a4 
D PtT4
-0.0199
0.1207
-0.1948
0.1690
a4 
DPtT4
-0.0279
0.0517
-0.1946*** 0.0556
D2)
Dumm -0.0224***
y 2
0.2551
R
-0.1160***
0.0233
-0.0259*
0.3939
a1
a1
a2
a2
0.4064***
0.0066
0.4291
0.0149
20
F test results (table 4 continued)
Test stat.
(d.f.)
Null hypothesis
b0

= b0
n
 3)
n
 bi  =
b
a
a
i 0
n
i 1

i
i 0
n
=
i 1
n
b
b
i n0
i 0
n
i
n1
i 1

i
i

9.700
(1,693)
0.001
18.237
(1,693)
0.000
Test stat.
(d.f.)
0.322
(1,348)
0.293
(1,348)
1.344
(1,348)
Test stat.
(d.f.)
Pr(|F|>c)
0.5887
2.919
(1,240)
0.088
0.2471
0.0263
(1,240)
0.871
Pr(|F|>c)
0.570

0.8692
1.7791
1.0455

0.4242
1.6058
1.6488

0.0229
-0.7201
-0.5171
0.4064
-0.4222
-0.5679
i
i
a
a
Pr(|F|>c)
i
i

1) The levels of statistical significance are denoted with *for 1%, ** for the 5% and *** for
the 1%.
2) Dummy variable is set to 1 when terminal price is lower than shipping point price


3)H0: b0 = b0 is not tested when one of the estimated coefficients is not statistically
significant
21
Table 5. Summary of asymmetry test results
Cumulative
short term
shipping point price 
terminal price
shipping point price 
terminal price
previous terminal price
 current terminal
price
Apples
Positive APT
positive APT
Negative APT
table grapes
No APT
No APT
No APT
Peaches
Negative APT
Inconclusive
No APT
Table 6. Tests of asymmetry using quantile regressions
Short term
Apples
Table
grapes
Peaches
Cumulative
shipping point
previous terminal
price  terminal
price  current
price
terminal price
Negative APT
Negative APT
Level of
Quantile
shipping point price 
terminal price
20%
Negative APT
40%
No APT
Negative APT
Negative APT
60%
-
-
-
80%
Positive APT
Positive APT
No APT
20%
Negative APT
Negative APT
No APT
40%
No APT
No APT
No APT
60%
Positive APT
Positive APT
No APT
80%
Positive APT
Positive APT
No APT
20%
No APT
No APT
No APT
40%
Negative APT
No APT
No APT
60%
Positive APT
No APT
No APT
80%
No APT
No APT
No APT
22
Appendix
DATA DETAILS
Fresh apples:
 Data period: from Jan 10, 1998 to Oct 1, 2011
 Variety: red delicious
 Unit: $/pound
 Other details:
o Retail prices: region=Northwest of U.S.;
o terminal prices: region=Seattle, grade=WaExFcy, product origin=Washington,
size=88s or mid-range package=carton tray pack;
o Shipping point prices: region=Washington state, other specifications are the
same as what are reported in the terminal market.
Fresh peaches
 Data period: from 5/23/1998 to 2/1/2012
 Variety: “various yellow flesh available.”
 Unit: $/pound
 Other details:
o Retail prices: region=Northwest U.S.
o Terminal prices: region=Los Angeles, size=42s, package=carton 2 layer tray
pack
o Shipping point prices: region=Central and Southern San Joaquin Valley
California, size=40-42s, “preconditioned”.
Table grapes
 Data period: from 1/10/1998 to 12/242011
 Variety: red/white seedless
 Other details:
o Retail prices: region=Northwest U.S.
o Terminal prices: region=Los Angeles, variety=Thompson seedless, size=large,
product origin=California and imports, package=all containers
o Shipping point prices: regions=Coachella Valley and Chile imports
Fresh strawberries
 Data period: from 1/10/1998 to 2/18/2012
 Unit: $/lb
 Other details:
o Retail prices: region=Northwest of U.S.
23
o Terminal prices: region=Los Angeles, size=medium to large, origin=Oxnard and
Salinas–Watsonville, package=flats 12-pt baskets
o Shipping point prices: region=Oxnard and Salinas–Watsonville, and other
specifics are the same as reported in terminal market.
Quantile Estimation results: Apples
40%
quantile
20%
quantile
Coefficient1)
Std. Error
Std. Error
Coefficient1)
0.0000
0.0000 0.0000
0.0000

D Pt S 0.0000
0.0037 0.0000

D Pt S 0.2500***

Na
0.0000
0.0001
0.0010
Na
1.3636*** 0.0266
0.0837 0.0437
0.0941
Na
0.0000
D Pt S1 0.0000
0.0053 0.0000
0.0013
Na
0.3030*** 0.0933

DPt S1 0.2500
0.2595 0.2044*** 0.0091
Na
0.0000
0.0207

D PtT1 0.0000
0.0027 0.0000
0.0007
Na
0.0909
0.2034

DPtT1
0.1461 0.4782*** 0.0133
Na
0.0000
0.0175
0.0001
Na
-0.0076
0.0051
Pr(|F|>c)
Test stat.
(d.f.)
Test stat.
(d.f.)
Pr(|F|>c)
0.010
Na
0.000
Na
b0
b0
b1
Std.
Error
Std. Error
Regressor

b1
80%
quantile
Coefficient1)
Coefficient
a1
a1
Dumm 0.0000
0.0003 0.0000
y
F test results
D2)
Test stat.
(d.f.)
Null hypothesis
b0

= b0
n
n
0.0000
0.0000
Na

0.5000
0.2480
Na
0.0000

0.0000
0.0000
Na
0.0909

0.8750
04782
Na
0.0000
a

i 0
n
=
i 1
n
b
b
a
a
i n0
i
n0
i
n1
i
i
i

i
i

7.775
(1,693)
35.934
(1,693)
0.005
0.000
6.600
(1,693)
1295
(1,693)
Pr(|
F|>c
)

a
i
Test stat.
(d.f.)
233.5
(1,693)
0.195
(1,693)
1.666
b
i 0
n
Pr(|F|>c)
 3)
 bi  =
i 1
0.8750***
Coefficient1)
60%
quantilee
0.0216
0.000
0.658
i
i 1 levels of statistical significance are denoted with *for 1%, ** for the 5% and *** for
1) The
the 1%.
2) Dummy variable is set to 1 when terminal price is lower than shipping point price


3)H0: b0 = b0 is not tested when one of the estimated coefficients is not statistically
significant
24
Note: Estimation at 60% quantile was not possible because of data limitation.
25
Quantile Estimation results: Table grapes
40%
quantile
20%
quantile
Coefficient
Coefficient1)
Regressor

-0.0141***


Coefficient1)
Std. Error
Coefficient1)
Std. Error
Coefficient1)
Std. Error
0.0041
-0.0008
0.0036
0.0038
0.0039
0.0183***
0.0048
0.2322
0.8187***
0.1213
1.0969***
0.0954
0.1698
0.3291*
0.1723
0.4048**
0.2027
0.1103
0.2354
0.2080
0.9487***
0.1488
0.6977***
b1

b1

b2

b2

b3
b3
b4 
b4 

a1

a1

a2

a2
a3
a3
a4 
a4 
D Pt
D Pt S
D Pt S1
DPt S1
D Pt S2
D Pt S2
D Pt S3
D Pt S3
D Pt S4
D Pt S4
D PtT1
DPtT1
D PtT2
DPtT2
D PtT3
DPtT3
D PtT4
DPtT4
D2)
Dummy
b0

b0

80%
quantile
Std. Error
0.4881**
S
60%
quantile
0.1284
0.1088**
0.0474
0.1028
0.0995
0.2269**
0.5527***
0.1567
0.3516***
0.0805
0.2715
0.1761
0.2081
0.1329
0.1428
0.0895
0.0654
0.0532
0.1722*
0.0995
0.3806***
0.0939
0.1672
0.1360
0.1551
-0.0893
0.1577
-0.1655
0.1783
0.1493
0.1715
0.1240*
0.0674
0.1338*
0.0789
0.2456**
0.0949
0.1171
0.1566
-0.0031
0.0713
0.0429
0.0740
0.1554
0.1108
0.0240
0.0767
0.0056
0.0547
0.0601
0.0587
0.0718
0.0494
-0.0581
0.0716
0.0221
0.0577
0.0414
0.0646
0.0484
0.0910
-0.0553
0.0388
-0.0942**
0.0373
0.0177
0.1840
0.1040
0.0787
-0.1322*
0.0793
-0.0556
0.0435
-0.0351
0.0435
-0.1275
0.1021
0.0565
-0.2068
0.0418
-0.0477
0.3621
**
-0.1382
0.0928
-0.0420
0.0380
-0.0966*
-0.0932**
0.0412
-0.0360
0.0335
-0.0016
0.0402
-0.0275
0.0841
-0.1595
0.1632
-0.1684**
0.0655
-0.1844***
0.0609
-0.1155**
0.0509
0.0346
0.0415*
0.0251
0.0176
0.0500
0.0071
0.0437
-0.0125
***
-0.0152
0.0625
0.0695
0.0679
0.1116**
0.0466
0.0261
0.0956
-0.0012
0.0478
-0.0060
0.0382
-0.0063
0.0229
-0.0113
0.0547
-0.0367
0.0381
-0.0255**
0.0106
-0.0407***
0.0146
-0.0563***
0.0134
Test stat.
(d.f.)
Pr(|F|>c)
Test stat.
(d.f.)
Pr(|F|>c)
Test stat.
(d.f.)
Pr(|F|>c)
F test results
Test stat.
(d.f.)
Null hypothesis
b0

= b0
n
b
i 0

i
 3)
n
b
=
i 0
n
a
i 1
i 1
n
b
b
a
a
i n0
i n 0
i
n1
i 1

8.909
(1,348)
0.003

0.2031
(1,348)
0.652
i
n
 ai  =
Pr(|F|>c)
i
0.460
(1,348)
1.236
(1,348)
1.244
(1,348)
0.497
0.267
0.265
4.750
(1,348)
4.437
(1,348)
0.344
(1,348)
0.030
0.036
0.557
8.986
(1,348)
21.515
(1,348)
0.019
(1,348)

0.5039
0.7918
1.2876
2.0218

1.9225
1.2042
0.5957
0.6512

-0.3681
-0.2350
-0.1517
-0.1922
-0.2390
-0.0561
-0.0254
-0.1592
i
i
i
i

0.003
0.000
0.890
1) The levels of statistical significance are denoted with *for 1%, ** for the 5% and *** for
the 1%.
2) Dummy variable is set to 1 when terminal price is lower than shipping point price
26

3)H0: b0 = b0
significant

is not tested when one of the estimated coefficients is not statistically
27
Quantile Estimation results: Peaches
Coefficient
Regressor

-0.0093**
D Pt S 0.1360
D Pt S 0.2333
**
D Pt S1 0.4703
***
DPt S1 0.8956
D Pt S2 0.2039
D Pt S2 0.0381
D Pt S3 0.2582
*
D Pt S3 0.2883
**
D Pt S4 0.2788
**
D Pt S4 0.2499
D PtT1 -0.2877
DPtT1 0.0571
**
D PtT2 -0.4044
DPtT2 -0.1046
D PtT3 -0.0511
DPtT3 -0.1888
D PtT4 -0.0584
DPtT4 -0.0979

b0

b0

b1

b1

b2

b2
b3
b3
b4 
b4 

a1

a1

a2

a2

a3
a3
a4 
a4 
Dum
my
D2)
Null hypothesis
b0

= b0
n
b
a
in 0
i n0
 ai  =
i 1
n
 bi 
i n0
b
a
a
i n 0

i
-0.0221
Std. Error
0.0046
40%
quantil
Coefficien
t1) e
-0.0008
Std. Error
60%
quantil
Coefficien
t1) e
Std. Error
80%
quantil
Coefficien
t1) e
Std. Error
0.0034
0.0025
0.0035
0.0201**
0.0082
0.0846
0.1214
0.1611
0.1408
0.0914
0.0897
0.1570*
0.2564
0.3402**
0.1501
0.1791
0.1406
0.2617
0.1652
0.2046
0.5144***
0.0880
0.4995***
0.1102
0.7591***
0.1483
0.2203
0.6243***
0.1636
0.4765***
0.1789
0.4048*
0.2437
0.2111
0.0595
0.1160
0.2744
0.2157
0.1231
0.3128
0.2267
0.1323
0.1403
-0.0394
0.1091
0.1279
0.1316
0.1695
0.1389
0.1328
0.0420
0.1170
0.0002
0.3101
0.1695
0.1188
0.0813
0.0934
0.1026
0.1385
0.1510
0.1127
0.1751
0.1271
0.1114
0.1126
0.1418
0.1886
0.1211
-0.0056
0.0741
-0.0028
0.0642
0.1610
0.1748
0.3924
0.0045
0.0597
-0.0270
0.0577
0.2944
0.6304
0.2033
0.0657
0.1086
0.0985
0.1000
-0.0974
0.1627
0.1851
-0.3004
0.1820
-0.1920***
0.0705
-0.0203
0.3771
0.1406
-0.0249
0.0726
-0.0231
0.0862
-0.0918
0.0984
0.0751
0.0259
0.1398
0.1137
0.1134
-0.1048
0.1922
0.1204
-0.0272
0.0674
-0.0431
0.0675
-0.0995
0.1193
0.1073
-0.0481
0.0994
-0.0038
0.0782
0.0877
0.2026
0.0407
-0.1809
0.1131
0.0838
-0.0860
0.0524
-0.0692*
0.0143
-0.0053
0.0108
-0.0130
0.0124
-0.0230
0.0174
Test stat.
(d.f.)
Pr(|F|>c)
Test stat.
(d.f.)
Pr(|F|>c)
Test stat.
(d.f.)
Pr(|F|>c)
F test results
Test stat.
(d.f.)
Pr(|F|>c)
 3)
n
 bi  =
i 1
20%
quantil
Coeffici
eent1)

i
i

0.582
0.446
(1,240)
0.9618 0.327
(1,240)
1.3471
0.901
0.343
(1,240)
0.671
0.413
(1,240)
0.9794
0.980
0.323
(1,240)
0.0922 0.7616
(1,240)
1.0842
0.006
0.936
(1,240)
1.482
0.225
(1,240)
1.1456
1.7051
1.2100
0.7067
1.0939
0.2570
0.8016
0.3180
0.1091
i
n1

i
0.3341
0.0725
0.0370
0.4696
1
1) Thei levels
of statistical significance are denoted with *for 1%, ** for the 5% and *** for
the 1%.
2) Dummy variable is set to 1 when terminal price is lower than shipping point price


3)H0: b0 = b0 is not tested when one of the estimated coefficients is not statistically
significant

i
28