




































In ternationa l
Scholars
Journa ls

 

African Journal of Agricultural Marketing ISSN 2375-1061 Vol. 8 (8), pp. 001-007, August, 2020. Available online at 
www.internationalscholarsjournals.org © International Scholars Journals 

 

Author(s) retain the copyright of this article. 
 
 

 

Full Length Research Paper 

  

An application of the von Cramon-Taubadel and 
Loy error correction models in analyzing 

asymmetric adjustment between retail and 
wholesale maize prices in Ghana 

 
Henry de-Graft Acquah* and Samuel Kwesi Ndzebah Dadzie 

 
Department of Agricultural Economics and Extension, University of Cape Coast, Cape Coast, Ghana. 

 
Accepted 12 February, 2020 

 
Previous studies analyzing asymmetric price transmission have been based on an econometric specification that is 
shown to be inconsistent with cointegration. This study draws on the concept of cointegration to implement the von 
Cramon-Taubadel and Loy error correction approach in analyzing retail-wholesale maize price transmission in Ghana. 
Asymmetries are modeled to affect the direct impact of price increases and decreases as well as adjustments to the 
equilibrium level. The analysis demonstrates that transmission between retail and wholesale maize prices in Ghanaian 
maize market is asymmetric. In accordance with common belief, retailers react more quickly to increasing wholesale 
prices than decreasing wholesale prices. 

 

Key words: Asymmetric adjustments, cointegration, error correction model. 

 
INTRODUCTION 

 
Recent empirical studies analyzing whether prices rise faster 
than they fall, have categorised the price dynamics into 
symmetric and asymmetric

1
 processes. Those processes for 

which the transmission differs accordingly to whether the 
prices are increasing or decreasing (i.e. asymmetric price 
transmission) are of keen interest. This asymmetric behavior 
of prices has been the focus of numerous studies in 
agricultural economics. Mohanty et al. (1995) provide 
empirical evidence for this asymmetrical price behavior in 
the international wheat market using variants of model 
specification. All these studies use various forms of an 
econometric specification introduced by Wolffram (1971) and 
refined by Houck (1977). However, this specification is not 
consistent with cointegration between the prices being 
studied. Funda-mentally, if the prices at different levels of 

the market are are cointegrated, then the Wolffram-Houck 
specification is an inappropriate means of testing for  
 
 
 
*Corresponding author. E-mail:  
henrydegraftacquah@yahoo.com. Tel: 00233245543956.  
 
 
1 By definition, asymmetry is an unreciprocal relationship between rises and falls 
in prices. e.g. Farm and retail prices

 

 
 
asymmetric transmission between these levels.  

In this article, tests for asymmetric price transmission 
that is consistent with cointegration is invoked and 
applied to the transmission of maize prices from the retail 
to the wholesale level in Kumasi in the Ashanti region of 
Ghana. 

 
RATIONAL FOR ASYMMETRIC PRICE 
TRANSMISSION 
 
Several factors which culminate in asymmetric price 
transmission have been proposed in the literature. First, a 
commonly cited source of asymmetric price transmission 
is market power (Kinnucan and Forker, 1987; Miller and 
Hayenga, 2001; McCorrisston, 2002; and Lloyd et al., 
2003). Oligopolistic processors, for example, might react 
collusively more quickly to shocks that squeeze their 
margin than to shocks that stretch it, resorting in asym-
metric short run transmission in an attempt to hide the 
exercise of market power behind the „confusion‟ created 
by major shocks, processors could also react less 
completely to the shocks that stretch their margins 
leading to asymmetric long run transmission.  

Similarly, asymmetric price transmission could result if 

file:///C:\Users\user\Documents\REPUBLICATION\AGRICULTURAL%20SCIENCES\AppData\Local\Temp\www.internationalscholarsjournals.org


 
 
 

 

traders in the local market believe that competitors will 
follow an increase in the local market prices as price in 
the central market rise, but that they will not respond to 
falling prices in the central market by granting an 
equivalent reduction. It is however important to mention 
that concentration is probably a necessary but certainly 
not a sufficient condition for the exercise of market power, 
as the theoretical and empirical evidence on the 
relationship between these two phenomena is 
inconclusive (Weaver et al., 1989; Goodwin, 1994). 
Within the oligopoly context, both positive and negative 
asymmetries are conceivable depending on the market 
structure and conduct. In this regard, several studies of 
market power and asymmetry that focus on specific 
markets deserve to be mentioned. Borenstein et al. 
(1997) analysed vertical price transmission for crude oil to 
gasoline prices, and concluded that downward stickiness 
of retail prices for gasoline in an oligopolistic environment 
will lead to positive asymmetry. Alter-natively, Ward 
(1982) suggested that market power can lead to negative 
asymmetry if oligopolists are reluctant to risk losing 
market share by increasing output prices. Similarly Bailey 
and Brorsen (1989) considered firms facing a kinked 
demand curve that is either convex or concave to the 
origin. If a firm believes that no competitor will match a 
price increase but all will match a price cut (concave), 
negative asymmetry will result. Alternatively, if the firm 
conjectures that all firms will match an increase but none 
will match a price cut (convex), positive asymmetry will 
result. Hence, it is not clear a priori whether market power 
will lead to positive or negative asymmetry (Bailey and 
Brorsen, 1989). 
 

Secondly, price asymmetry can be partly attributed to 
adjustment cost that arises when firms change their 
quantities and prices of inputs and outputs. 
Consequently, positive or negative asymmetric price 
transmission results if these costs are symmetric with 
respect to increase or decrease in quantities or prices. In 
an analysis of the US beef market, Bailey and Brorsen 
(1989) argued that firms may face different adjustment 
cost depending on whether prices are rising or falling. 
Subsequently, they noted that the competition between 
meat packers faced with a high fixed cost and excess 
capacity, for example, might result in farm prices that are 
bid up rapidly, in response to increased demand for meat 
products, but fall more slowly as demand weakens. Ward 
(1982) suggested that retailers of perishable products 
may be hesitant to raise prices for fear that they could 
end up holding spoiled stocks, leading to negative asy-
mmetry. Heien (1980) disputes this assertion and notes 
that changing prices is less of a problem for perishable 
products than it is for those with a long shelf life, because 
for the latter, changing prices incur higher time cost and 
loss of good will. Thus, echoing the so called menu cost 
hypothesis proposed by Barro (1972), (that is a change in  
nominal price induces cost for example, the reprinting of 
price list or catalogues and the cost of informing market 
partners). Ball and Mankiw (1994) developed a model 

 
 

  
 
 

 

based on menu cost (the cost involved in changing 
nominal prices such as the cost of reprinting catalogues 
etc) in combination with inflation that leads to asymmetry. 
In this model, positive nominal input price shocks are 
more likely to lead to output price adjustment than 
negative price shocks. This is because in the presence of 
inflation, some of the adjustment made necessary by an 
input price reduction is automatically carried out by 
inflation, which reduces the real value of the margin. Thus 
in situations where firms face menu cost and inflation, 
shocks that bring upward price adjustment are rapidly 
responded to than those that reduce it, as inflation in this 
respect would have automatically affected some of the 
adjustment made necessary by the downward adjustment 
shocks (Kuran, 1983; Buckle and Carlson, 2000). In 
contrast to Bailey and Brorsen (1989), Peltzman (2000) 
makes a case for positive asymmetry affirming that it is 
easier for firm to disemploy inputs in the case of an 
output reduction than it is to recruit new inputs to increase 
output. This recruitment will lead to search cost and price 
premier increasing phases. Additional explanation for 
price asymmetry which has been proposed cannot be 
considered directly under market power or adjustment 
cost. Kinnucan and Forker (1987) suggested that 
asymmetry could result from government intervention, 
indicating that such political intervention can lead to 
asymmetric price transmission if it leads wholesalers or 
retailers to believe that a reduction in farm prices will only 
be temporary because it will only trigger government 
intervention, while an increase in farm prices is more 
likely to be permanent. 

 

MATERIALS AND METHODS 
 
Econometric models of asymmetric price transmission 
 
The modeling of asymmetric price transmission can be grouped into 
pre-cointegration and cointegration approaches (Meyer and von 
Cramon, 2004). The pre-cointegration and the cointegration 
approaches draw heavily from Houck (1977) and von Cramon 
(1998) respectively.  

Within the context of the pre-cointegration approaches, numerous 
authors have developed a test for asymmetric price transmission 
which is based on the Houck‟s segmentation of prices into 
increasing and decreasing phases (Kinnucan and Forker, 1987; 
Bailey and Brorsen, 1989; Zhang et al., 1995; Mohanty et al., 1995; 
Boyd and Brorsen, 1998). These different applications are 
considered as variants of the Houck‟s model and denoted by 
Houck‟s approaches. These pre-cointegration approaches require 
the data to be stationary in order to avoid spurious regression. The 
cointegration approaches are motivated by the fact that the Houck‟s 
approaches are not consistent with cointegration between the price 
series involved. The cointegration approaches draws heavily from 
(Granger and Lee, 1989; von Cramon-Taubadel, 1998; von Cramon 
- Taubadel and Loy, 1999). 

 

Houck’s specification 
 
Asymmetric Price Transmission has been tested in a wide variety of 
agricultural markets. Appel (1992) finds that both speed and degree 
of price transmission from the producer to the retail level for broilers 



 
 
 

 
in Germany is asymmetric. Boyed and Brorsen (1988) studied the 
US pork market and find no evidence of asymmetric price 
transmission. However, this result was challenged by Hahn (1990) 
who finds that prices at all levels of the US pork and beef marketing 
chains are more sensitive to price increasing shocks than to price 
decreasing shocks. Hansmire and Willett‟s (1992) indicated that 
farm-retail price transmission for New York state apples is 
asymmetric and Kinnucan and Forker (1987) came to the same 
conclusion regarding dairy product transmission in the United 
States. Pick et al. (1990) finds evidence that short-run but not long-
run vertical price transmission on the US citrus market is 
asymmetric. Finally, Ward (1982) points to both short and long run 
asymmetries in vertical price transmission for fresh vegetable in the 
United States, while Zhang et al. (1995) noted that price 
transmission for pea nut to peanut butter prices in the US is 
asymmetric in the short-run, but symmetric in the long-run.  

Each of these studies implements some variant of an 
econometric technique for estimating irreversibility that was 
introduced by Wolfram (1971) in response to work on irreversible 
supply reaction by Tweeten and Quance (1969). In investigating the 
relationship  between  an  output  price P and  input price P  , 

A B  
Tweeten and Quance (1969) used an indicator variable to split the 
input price into two parts: one variable includes only increasing 
input prices P


 and another includes only decreasing input 

B 

prices P− . From this, two input price adjustments coefficients (that 
B  

is β1


   and β1
−  ) can be estimated as specified below. 

P 
A  , T 

   β 
O 
  β   P   β −  P  −   ε 

T 
 

   1B,T  1B,T  
  

(1) 

 

Symmetric price transmission is rejected if the coefficients β1

   and  

β1
−  are significantly different from one another. Based on 

Tweeten 
 
and Quance (1969), Wolffram (1971) proposes a variable splitting 
technique that explicitly includes first difference of prices in the 
equation to be estimated which was later modified by Houck (1977). 
Within the context of the Wolfram-Houck (W-H) method, the 

 
 

 
Kinnucan and Forker, 1987; Pick et al., 1990; Zhang et al., 1995) 
are characterised by first-order autocorrelation, which is often 
symptomatic of spurious regression in the analysis of non-stationary 
time series (Granger and Newbold, 1974). Spurious regression is 
avoided if the analysed variables are cointegrated (Banerjee et al., 
1993). However, it can be shown that the W-H specification in (2) is 

fundamentally incompatible with cointegration between PA and PB . 

To see this, reparametrise (2) using the identity: 
 

∑ ΔPT ∑ ΔPB


,T ∑ ΔPB
−

,T   ≡ PB,T   − PB,0 
 

(3)  
And be rearranged to yield (Ward 1982): 
 

P  (P  β β − P ) β − P  (β − β − )   ΔP

 ε (4) 

A,T A,0 O 1    B,0 1    B,T 11∑B,T T 
 

This reparametrization of Equation (2) was proposed by Ward 

(1982) who tests whether the coefficient ( β1

 − β1

− ) differs 

from 0 in order to test whether price transmission is asymmetric.  
Von Cramon-Taubadel (1998) asserts that the estimation of 
equation 4 can lead to four basic results depending on the 

significance of the term ( β1

  − β1

− ) and the stationarity 

of the 

error term ε 
T 

: These are (i) β  − β − ≠ 0  (asymmetry) and ε 
T 

is 
 

      1 1            
 

I(0), (ii)   β  − β − 0 (symmetry) and ε 
T 

is I(1),   (iii) 
 

    1  1              
 

β − β − ≠ 0  (asymmetry) and ε 
T 

is I(1), (iv) β − β −  0 
 

1 1            1  1    
 

(symmetry) and  ε 
T 

is I(0). (i) implies that P  , P  and ∑ 
ΔP 

 

          A B      B ,T 
 

are cointegrated, which precludes cointegration between 

P
A  and 

 

P alone.  (ii)  and (iii)  are spurious regressions involving  non 
 

B                     
  

stationary variables (Granger and Newbold, 1974), while (iv) implies 

that  P and P are cointegrated. Notably, if the Houck method 
A B  

points to asymmetry, then either the results reflect spurious 
regression (iii), or the prices in question are not cointegrated (i). 
 

response of price  P to another price P 
A B 

following equation.  

T T 

∑ Δ PA , T β ο β 1  ∑ Δ PB


, T β 
T1 T1 

  
 

is estimated with the The asymmetric error correction representation 
 

  Fundamentally,  the  asymmetric  error  correction  model  (ECM) 
 

T  approach  is motivated  by  the  fact  that  all  the  variants  of  the 
 

 

aforementioned  Houck  approach  discussed  above  are  not 
 

∑ΔPB
−

,T  ε T 
 

consistent with cointegration between the price series. If the prices 
 

T1 (2) P and P are  cointegrated,  then  an  error  correction 
 

  A  B  
   

Where ΔP   and ΔP −   are the positive and negative changes in 

Prespectively, β 
O 

, β , β − are coefficients and   T   is the 
 

B 1  1  
 

current period.      
 

 
Numerous studies estimate a dynamic variant of the Houck‟s static 
model. Some analyst distinguish between short-run and long- 
asymmetries by introducing lagged terms in ΔP


 and ΔP − 

B,T B,T  

into  Equation  (1),  in  which  case β


 and β − become  lag 
 
polynomials. Long-run symmetry is tested by determining whether 
the sums of the coefficients in these polynomials are identical.  

Estimation of the above equation has generally taken place 
without adequate regard to the time series nature of the data used. 
Many of the empirical applications cited above (Appel, 1992; 

 
representation exists (Engle and Granger, 1987). Granger and Lee 
(1989) propose a modification to the error correction representation 
that makes it possible to test for asymmetric price transmission 
between cointegrated variables. This involves a Wolffram–type 
segmentation of the error correction term into positive and negative 
components. The asymmetric ECM takes the form:  

ΔP P

ECT


  −ECT− ΔP  ΔP

  
A,T ο 1 B,T  T−1 2 T−1  B,T −1  A,T−1  

(5) 

The error correction model (ECM) then relates changes in PA to 

changes PB as well as the so called error correction term (ECT =  
PA,t–ßo–ß1 PB,t), the Lagged residuals derived from estimation of 
their long run relationship. The ECT measures the deviation from 



 
 

 

the long-run equilibrium between the P and P  , and including it in 
A B  

the ECM allows PA not only to respond to changes in PB but also to 

correct any deviations from the long-run equilibrium that may be left 

over from previous periods. Splitting the ECT into positive and 

negative component (that is positive and negative deviation from 

the long-run equilibrium ( ECT and ECT − ) makes it possible to 

test for asymmetric price transmission.  
Von Cramon-Taubadel and Loy (1996) also segmented the 

contemporaneous response term in equation (5). This leads to the 

following specification in which contemporaneous and short–run 

response to departures from the cointegrating relation are 

asymmetric if β 1
 ≠ β 1− and β


 ≠ β2 − respectively: 

 

ΔP  β 
ο 
 β


 ΔP


  β − ΔP −  β 


ECT


  β − ECT − 

T −1 
 

 

 A , T    1 B , T 1B,T  T −1 2  
 

β ΔP   β ΔP   ε      
 

 B,T −1    A,T −1      (6)  
             

  
 
Noticeably, Equation 6 is equivalent to the Houck approach given 
by equation 2,  except that equation 6 also 
contains β ECT

 , β −ECT − 
,
 β ΔP , β ΔP . Thus in effect 

  T −1 2 T −1  B,T −1  A,T −1    
the asymmetric ECM with complex dynamics nests the Houck‟s 
model in first difference or has the structures of the Houck‟s model. 

 

DATA ANALYSIS AND RESULTS 

 

The application of the von Cramon Taubadel and Loy 
ECM is based on 520 weekly observations of undeflated 
(norminal) retail and whole sale prices for maize from 
January 1994 to December, 2003 from Kumasi in the 
Ashanti Region of Ghana were used in this analysis. The 
weekly data for all prices are cedi per 100 kg and given 
the high level of inflation in the period covered, prices are 
deflated using consumer price index (CPI) deflator. The 
source of the data is the ministry of agriculture in Ghana,  

The price transmission analysis proceeded with a 
granger causality test aimed to establish the direction of 
price linkage. The Granger causality test reveals in Table 
1 that the wholesale prices Granger causes the retail 
prices and the reverse is not valid. This necessitates the 
use of the single equation.  

According to the Augumented Dickey Fuller method 
(Dickey and Fuller, 1979) and Philip Peron (PP), the time 
series of the variables under consideration are non 
stationary integrated of the order one (Tables 2 and 3) 
and subsequently, a linear combination will result to a 
stationary series. This result has to be tested with the 
cointegration technique. The two step residual-based test 
by Engle and Granger (1987) was applied to confirm this 
assertion. The first step is the cointegrating regression of 
non stationary price series between the retail as 
dependent against the wholesale as independent. 
 

P R  β 0  β 1 PW   ε T 

 

Where: 
 
PR = the retail price 

 
 

  
 

 

PW  = the wholesale price, 

ε T = error term 

 

The second step involves testing whether the residuals 
from the cointegrating regression are non stationary by 
using ADF test and PP test. 
 

ε T  PR    − β 0   − β 1 PW U T 

 

Where UT    is the error term. 

 

The co integrating results for the first step is shown in the 
upper part of Table 4 with it resultant unit root test of the 
residuals in the lower part of Table 4. With the results of 
the Engle Granger cointegration technique below, it can 
be confirmed that the retail and wholesale prices are 
cointegrated.  

Information criteria such as the Akaike Information 
Criterion, (Akaike, 1973) and the Bayesian Information 
Criterion (Schwarz, 1978) are applied to determine the 
number of lags to be included in all models. This study 
finds significant asymmetries in the adjustment of retail 
prices in response to wholesale prices when the price 
transmission process is analyzed using the von Cramon-
Taubadel and Loy asymmetric error correction model. 
The result of the test for asymmetry is presented in the 
analysis of variance displayed in Table 5 in which the 
symmetric model specified in equation 7 is compared with 
the asymmetric model specified in equation 8. 

Δ P
A,T   β ο 

  β
 
1   Δ  

P
 B  , T   β     E  C  TT  − 1 

 

  β  Δ P B  , T − 1   β  Δ  P A  , T − 1   ε  (7) 
 

Δ P 
A , T 

  β 
ο 
  β  Δ P   β  − Δ P −  β ECT 

T − 1 
 

 

     1  B , T  1  B , T     
 

β −ECT −   β 
 
Δ P 

B ,T −1 
 β 

 
Δ P 

A,T−1 
  ε   

 

 2   T − 1        (8)  

                   
 

 

The results of the model estimations are displayed in 
Table 6 in appendix and the asymmetric adjustments 

coefficients of interest are (9.031e-
01

, 6.964e-
01

) and (-

3.156e-
02

,-1.938e-
01

) for the short run and long run 
 
adjustment parameters respectively. 
 

The obvious difference between the values of the 

coefficients for the positive and negative partitions in the 

model culminates in rejection of the null hypothesis of 

symmetric transmission via a conventional F test. 
 

It can be concluded that that asymmetry existed under 
the von Cramon-Taubadel and Loy ECM. The formal test 
of the asymmetry hypothesis using Equation (8) is: 

H 
0 

: β

   β  −    and β


 − 

 

  1  2 
 

 
In effect asymmetric behavior is detected by a joint F-test. 
We hypothesis the effect of increase and decrease in 
wholesale price on the retail price was the same on the 



     
 

 Table 1. Granger causality test.    
 

       
 

  Market Effect Hypothesized cause F statistic p-value 
 

  
Kumasi 

Retail price Wholesale price 3.659 0.03 
 

  
Wholesale price Retail price 0.462 0.63 

 

   
 

 
 

 
Table 2. Results of unit root test in levels of maize prices in Kumasi market.  

 
 Market/Test None P- value Intercept P-value Intercept and trend P-value 

 Kumasi wholesale price       

 ADF test -1.3 0.1709 -4.4 0.0004 -4.4 0.0021 

 PP test -1.3 0.1923 -4.4 0.0003 -4.5 0.0016 

 Kumasi retail price       
 ADF test -1.3 0.1839 -4.4 0.0043 -4.3 0.0021 

 PP test -1.3 0.2269 -4.4 0.0004 -4.4 0.0025 
 
 
 
 
Table 3. Results of unit root test in differences of maize prices in Kumasi market.  
 

 Market /test None P- value Intercept P-value Intercept and trend P-value 

 Kumasi wholesale price       

 ADF test -24.1 0.000 -24.0 0.000 -24.0 0.000 

 PP test -24.1 0.000 -24.0 0.000 -23.8 0.000 

 Kumasi retail price       
 ADF test -24.2 0.000 -24.2 0.000 -24.2 0.000 

 PP test -24.5 0.000 -24.5 0.000 -24.5 0.000 
 
 
 
 

Table 4. Engle Granger test for maize.  
 

Results of 1
st

 stage test for maize   
Market pair name Constant Coefficient P-value for  

Kumasi retail -wholesale 63218.68 0.905705 0.0000  

Results of 2nd stage test for residuals     

Market name ADF Test P-value PP test P- value 

Kumasi -6.0515 0.0000 -5.7440 0.0000 
 
 
 
 

Table 5. Testing for asymmetry using an analysis of variance.  
 

 Model Res. DF RSS DF Sum of Sq F Pr(>F) 

 Symmetric 498 1.0521e + 11     

 Asymmetric 496 1.0330e + 11 2 1.9130e + 09 4.5926 + 0.01056 * 
 

Significance codes: 0 „***‟ 0.001 „**‟ 0.01 „*‟ 0.05 „.‟ 0.1 „ ‟ 1. 



 
 
 

 

retail price was the same. The F-test indicates that the 
null hypothesis of symmetric transmission is rejected at 
5% level or lower. The p-value of 0.01056 indicates that 
the null can be rejected here, suggesting the existence of 
significant asymmetry. Intituitively, this implies that the 
positive and negative components of the error correction 
term and the increasing and decreasing components of 
the wholesale price can be treated separately in the 
model. This asymmetric result suggests that the retailers 
react more quickly to increasing wholesale prices than to 
decreasing wholesale prices. This finding is derived on 
the basis of the von Cramon-Taubadel and Loy error 
correction model. 
 

 

Conclusion 

 

This research analyzed the behavior of tests of asy-
mmetric price transmission according to the von Cramon-
Taubadel and Loy ECM approach for retail and wholesale 
prices in the Ghanaian maize market. The findings 
suggested that the retail-wholesale price transmission 
process for maize in Kumasi was asymmetric. In accor-
dance with common belief, the adjustment of retail price 
to the wholesale price is faster when there is an increase 
in the wholesale price than when there is a decrease. 
Further research will be necessary to establish whether 
this asymmetric behavior exist in other agricultural 
markets. 
 

 
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APPENDIX 

 
Table 6. The results of the model estimations.  

 
Coefficients Standard error   

Intercept 
ΔP


 

W ,T 

ΔP − 
W ,T 

ΔP
,−1 

W T 
ΔP

,−2 
W T 

ΔP
,−3 
W T 

ΔP
,−4 

W T 
ΔP

,−5 
W T 

ΔP
,−6 

W T 
ΔP

, −1 
R T 

ΔP
, −2 

R T 
ΔP

, −3 
R T 

ΔP
, −4 

R T 
ΔP

, −5 
R T 

ΔP
, −6 

R T 
 

ECTT −1  

ECT −T −1 
 

Multiple R
2
 

2 
Adjusted R 

 

BIC 
 

Durbin Watson stat. 

  
-2.901e

+03
  

9.031e
-01

 
 

6.964e
-01

 
 

1.213e
-01

 
 

9.052e
-03

 
 

1.542e
-01

 
 

2.221e
-01

 
 

4.160e
-02

 
 

1.016e
-01

 
 
-1.154e

-01
 

 

4.835e
-02

 
 
-1.492e

-01
 

 

-1.430e
-01

 
 
-3.070e

-02
 

 
-1.258e

-02
 

 
-3.156e

-02
 

 
-1.938e

-01
 

 
0.5084 

 
0.4926 

 
11300.72  
11376.2  
2.0211  

  
-1.295e

+03
  

6.655e
-02

 
 

4.807e
-02

 
 

5.292e
-02

 
 

5.170e
-02

 
 

5.018e
-02

 
 

5.009e
-02

 
 

5.099e
-02

 
 

5.013e
-02

 
 
4.649e

-02
 

 

4.568e
-02

 
 

4.448e
-02

 
 

4.350e
-02

 
 
4.381e

-02
 

 

4.309e
-02

 
 

3.578e
-02

  
6.139e

-02
 


