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Product differentiation and dynamic price behavior in fish markets.

Abstract

The objective of this paper is to estimate the dynamics of aquaculture and fish prices as a response to price shocks. The vector autoregression approach will be used to explain the dynamics of the sea bream market in both cultured and wild fishing. The main result is that changes in public regulation or in production conditions could stimulate production responses which may take time to settle. Usually, the change is a matter of adjusting between equilibria over a period of time, with the pattern and speed of the adjustment, depending on the nature and degree of disequilibrium in the fishing system. (JEL Q10, Q20)

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Introduction

Economic relationships among aquaculture output prices and fishery prices are intertwined and complex. In particular, it is difficult to accurately determine whether the substitution or the complementary effects will be dominant in explaining the relationship between cultured and wild sea bream prices. Changes in public regulation or in production conditions could stimulate production responses that may take time to settle. Usually, the change is a matter of adjusting between equilibria over a period of time, with the pattern and speed of the adjustment depending on the nature and degree of disequilibrium in the fishing system. In this paper, the vector autoregression approach will be used [Sims, 1980] to explain the dynamics of the sea bream market in both cultured and wild fishing.

The main purpose of this paper is to estimate the dynamics of aquaculture and fish prices as a response to price shocks. The dynamics of the sea bream (Sparus Aurata) market, in both cultured and wild fishing, will be analyzed using the vector autoregression approach. This approach will be used for analyzing the dynamic impact of random disturbances on this system of variables.

Sea bream is present in the Spanish markets only as a fresh product and is always sold in whole form. The individual market size of farmed sea bream is usually around 400-500 grams. The size of wild bream used to be more heterogeneous and generally bigger than farmed fish. Small sizes are usually served whole, while bigger sizes are cooked whole but served in portions and considered more luxurious products and higher in price.

Cultured sea bream may either be imported (mainly from Greece) or local, but there are no specific characteristics that makes it distinguishable for normal consumers. The wild product mainly comes from local landings. Sea bream experienced a sustained increase of supplies from 1993-2000, with reduction in prices from 1990-1996 (achieving certain stability after 1996). The positive variation in the supply of cultured fish has not been supported by promotion campaigns. Nevertheless, its presence in the restaurant sector and fish shops is much more common today than in the mid 1990s.

This paper is organized as follows. The next section briefly discusses the data and the econometric methodology that will be used to test the price dynamic hypothesis in sea bream markets. Then, the following section displays the econometric results and discussion. The final section presents some conclusions.

Data and Methods

Weekly data for cultured and wild sea bream prices are provided by the Barcelona Central Fish Market (Mercabarna). The time series include 79 observations from January 2000 until the end of June 2001. The time period and source are the same for sea bass, salmon, and sole prices, and are considered in the estimation model. Definitions of variables in the model can be found in Table 1.

In order to estimate the dynamics of aquaculture and fish prices as a response to price shocks, a Vector Error Correction (VEC) model will be estimated. The VEC model will be used for analyzing the dynamic impact of random disturbances on the system of variables [Hamilton, 1994]. Several applications of this methodology for the study of fish markets can be found in Guttormesen [1998], Guttormesen [1999], and Bene, Cadren, and Lantz [2000].

Unit root tests are performed, following Dickey and Fuller [1979] and Phillips and Perron [1988], to examine whether the variables are deterministic or stochastically non-stationary. In this paper, the Augmented Dickey-Fuller (ADF) test is based on a regression of the first difference of fish prices in period t on prices in period t - 1. If there is a unit root, the level variable [p.sub.t-1] should have a coefficient equal to zero. The ADF test is the t-statistic on [p.sub.t-1]. Critical values are not the well known values for the t-statistic, but rather the McKinnon [1991] critical values. If there is no unit root, then the price series are said to be stationary in levels or integrated of order zero (denoted I(0)). If there is a unit root but differencing the series once makes it stationary, then it is said to be integrated of order one (I(1)). The Phillips-Perron test is also a unit root test. However, unlike the ADF test, there are no lagged difference terms. Instead, the equation is estimated by ordinary least squares and the t-statistic of the eventual unit root coefficient is corrected for serial correlation [Hamilton, 1994]. Descriptive statistics of the variables in the model can be found in Table 2.

Results and Discussion

The unit root tests were performed including both: 1) a constant and 2) a constant and a linear trend. The tests were applied to the variables in logarithms. The results of the ADF and the PP test indicate that most of the series are integrated of order one (Table 3). It was not possible to reject the hypothesis that the data do not present non-stationary seasonality.

Given that the overall picture suggests that stochastic trends are present and all variables contain upward trends, the paper shows that these tests indicate that the price series are integrated of order one. The cointegrated system will be represented as the error correction vector. This specification is preferred because it analyzes the error from the long-run equilibrium relation and the correction caused by this error. A cointegrating regression can be interpreted as a long-run equilibrium relationship between the variables [Maddala and Kim, 1998]. Critical values clearly suggest the existence of one cointegrating vector for sea bream (Table 4), although the evidence in favor of a second cointegration relationship was not accepted. The first cointegrating vector for sea bream can be written as (all variables in logs, assuming linear deterministic trend in the data):

ln(SAC) = -26.988 + 0.849 * ln(SAW), (1)

where SAC and SAW are prices for cultured and wild sea bream, respectively.

Estimation of the Error Correction Model and Granger Causality

Under the constraint of a one cointegration relationship, the error correction mechanism (following the Johansen formulation) is a VEC(2) in differences. In the model, external variables such as the price of sea bass (Dicentrarchus labrax), salmon (Salmo salar), the price of sole (Paralichthys adspersus), and the dummy variables, account for the seasonality of the series.

The first step in applying the VEC model is to determine the correct lag length. The most parsimonious model with no autocorrelation was selected using the Akaike and Schwarz criteria (Table 5). According to these results, a lag length of two weeks is sufficient to yield a white noise residual. Causal ordering of the variables used in this paper stems mainly from empirical information about the markets. Once the VEC model has been specified, the validity of this assumed causal ordering will be tested.

Therefore, following Johansen [1988], two error correction models are estimated, one for cultured sea bream and another for wild sea bream. The estimated model for cultured sea bream is (values in brackets denote t-values):

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

The estimated model for wild sea bream is:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

The estimated model indicates that weekly changes in cultured sea bream prices depend mainly on its own past changes but that past changes in cultured sea bream prices are essential to explain the evolution of wild sea bream prices (Table 6). In fact, cultured sea bream prices appear to determine the evolution of wild sea bream prices more directly than the wild sea bream prices itself. The influence of sole, salmon, cultured sea bass (LC), and wild sea bass (LW) prices appear to be rather weak and poorly significant. On the other hand, seasonal effects are clearly significant both for cultured and wild sea bream, although coefficients present a different sign. Seasonal effects are measured with two dummy variables. D1 is the dummy to reflect the effects directly related to consumption during the second and third weeks of December. D2 is the dummy for the last week of December and the first week of January. The negative sign for D1 indicates that consumers are willing to pay a higher price for wild sea bream at Christmas time. This effect changes in the first week of January (the second part of the Christmas holidays). The positive effect is related to the cultured sea bream equation (2), while there is a negative effect for the wild sea bream equation (3).

The adjustment coefficient in the VEC equations presents a different sign and significance level for the cultured and wild sea bream. The difference between SAC and SAW is viewed as the error from the long equilibrium relation. The coefficient indicates the correction to the SAC price caused by this error. It can be interpreted as the correction to cultured sea bream prices that are caused by a deviation in the long-run equilibrium. As for the cultured sea bream prices equation (2), the coefficient is negative and significant. Hence, it could be assumed that when cultured sea bream prices are below its equilibrium level, then the adjustment will be upward. Regarding the wild sea bream equation (3), the speed of adjustment coefficient is positive and non-significant, indicating that the error correction term is less than normal. Therefore, it causes cultured sea bream prices to be higher than any given values of the other explanatory variables (Table 6).

Granger Causality

Granger causality definition [Granger, 1969] states that in the conditional distribution, lagged values of variable x add no information to explain the movements of variable y beyond that provided by lagged values of x itself.

The existence of causality was tested for sea bream, considering the existence of different lags length (between 1-20). In all cases, Granger causality has been characterized by a one-way causality (Table 7). The major finding is that in very few cases, wild fish prices will cause cultured prices.

Impulse Response Functions

This section reports the empirical results of impulse response functions derived from the estimated VEC model. An impulse response function determines the effect of a one-time shock to one of the innovations on current and future values of the endogenous variables and the path by which the variables return to the equilibrium [Greene, 2000].

A shock to the price of cultured sea bream not only affects the cultured sea bream directly but is also transmitted to other endogenous variables (in this case, wild sea bream) through the dynamic structure of the VAR. Figure 1 includes the estimated net contemporaneous and dynamic impacts over a 20 week period of a positive cultured sea bream price shock on cultured sea bream and wild sea bream. The line indicates estimates of the impulse response function.

Coefficients of the impulse response function to one standard deviation innovation can be found in Table 8. The response function does not return to zero in any case due to the existence of the unit root.

[FIGURE 1 OMITTED]

The effect of a positive cultured sea bream shock on cultured sea bream prices is expected to decline gradually and reach a steady state. However, a significant increase in price is registered in the first four weeks. Nevertheless, after the initial shock is over, the VAR model shows that the effects of positive cultured sea bream shock on wild sea bream prices gradually decline. The response of wild sea bream prices to a wild sea bream shock is positive but not persistent and declines after the second period. The initial response of wild sea bream to a cultured sea bream shock is positive until the third period. However, the effects are not persistent and decline to a stationary state.

Conclusion

In this paper, the price relationships between cultured and wild sea bream in the Spanish market have been investigated. The results show that although cultured and wild sea bream appear to be clearly cointegrated, VEC models present a rather weak adjustment process with relevant effects of seasonal dummies. Price links with salmon, sole, and sea bass are poorly significant. This implies that individual sea bream prices can vary substantially from prices of the rest of the competing species. Therefore, arbitrage across the different cultured and wild markets is not readily apparent in the data. This may reflect the inexistence of agreements between wild and cultured buyers and sellers in the different local markets. Perhaps, in each local market, sellers and producers have set up contacts and marketing arrangements to move products. Market sellers appear to be reluctant to alter these arrangements because of short term and perhaps transitory price shocks.
TABLE 1 Data Sources and Definition of the Variables

Variables  Definition

SAC        Price for Sea Bream (Sparus Aurata), cultured
SAW        Price for Sea Bream (Sparus Aurata), wild
SOLE       Price for Sole (Paralichthys adspersus)
SALMON     Price for Salmon (Salmo salar)
LC         Price for Sea Bass (Dicentrarchus labrax), cultured
LW         Price for Sea Bass (Dicentrarchus labrax), wild
D1         Dummy for second and third week of December
D2         Dummy for last week of December and first week of January

TABLE 2 Descriptive Variables

               SAC     SAW         SOLE       SALMON   LC      LP

Mean           0.696   1209          0.96     0.624    0.745   1209
Median         0.704   1240          0.929    0.623    0.756   1218
Maximum        0.788   1384       1225        0.758    0.826   1396
Minimum        0.557      0.815      0.84     0.548    0.638      0.984
Std. Dev.      0.0466     0.0989     0.0864   0.0564   0.0538     0.111
Skewness      -0.387     -1.611      0.957    0.352   -0.596     -0.0864
Kurtosis       2.665      6.258      3.283    2.056    2.351      1.793
Jarque-Bera    2.345     69.152     12.332    4.567    6.064      4.893
Probability    0.309      0          0.0021   0.101    0.0482     0.0865
Observations  79         79         79       79       79         79

                 D1         D2

Mean             0.0253     0.0253
Median           0          0
Maximum          1          1
Minimum          0          0
Std. Dev.        0.158      0.158
Skewness         6.043      6.043
Kurtosis        37.526     37.256
Jarque-Bera   4405       4405
Probability      0          0
Observations    79         79

Data source: Barcelona Central Fish Market. All variables in logs.

TABLE 3 ADF and PP Unit Root Tests

                         ADF                    PP
                                    Constant &               Constant &
Level Series             Constant   Trend       Constant     Trend

SAC                      -2.184     -3.267       -4.034       -7.18
SAW                      -2.773     -2.752       -2.702       -5.513

                         ADF                    PP
                                    Constant &               Constant &
First Difference Series  Constant   Trend       Constant     Trend

SAC                      -7.18(*)   -7.221(*)   -11.265(*)   -11.122(*)
SAW                      -5.513(*)  -5.473(*)    -6.0857(*)   -6.0264(*)

Notes: (*) McKinnon critical values for rejection of hypothesis of a
unit root.

TABLE 4 Johansen Cointegration Test for Cultured Sea Bream Weekly Price
Series & Wild Sea Bream Weekly Price Series

Eigenvalue  Likelihood Ratio  5 Percent Critical Value

0.105093      13.20495             15.41
0.060788       4.76624(*)           3.76

Notes: (*) Denotes rejection of the hypothesis of cointegration at the
5 percent significance level.

TABLE 5 Akaike (AIC) and Schwartz (SC) Criteria for Lag Selection of the
VEC Model

Lag (Weeks)   AIC      SC

 1            -3.607   -3.345
 2            -3.649   -3.426
 3            -3.601   -3.171
 4            -3.604   -3.0476
 5            -3.534   -2.849
 6            -3.458   -2.642
 7            -3.443   -2.495
 8            -3.536   -2.453
 9            -3.424   -2.203
10            -3.436   -2.0761
11            -3.331   -1.8297
12            -3.3102  -1.665

TABLE 6 Vector Error Correction Estimates

Cointegrating Equation

SAC                           1               -
SAW                          -0.1199          -
t                            -1.663           -
Constant                     -0.554           -
                               (1)           (2)
Error Correction:             D(SAC)        D(SAW)
Cointegrating Equation       -0.421         0.232
t                            -1.921         0.561
D(OC(-1))                     0.0404        0.457
t                             0.29          1.739
D(OC(-2))                     0.104         0.23
t                             1.074         1.25
D(OP(-1))                     0.0385        0.302
t                             0.596         2.479
D(OP(-2))                     0.001201     -0.252
t                             0.01921      -2.132
Constant                     -0.118         0.422
t                            -0.816         1.546
SOLE                         -0.0502       -0.048
t                            -1.363        -0.688
SALMON                        0.0636        0.0593
t                             0.734         0.362
LC(-1)                        0.136        -0.392
t                             0.833        -1.273
LW(-1)                        0.0202       -0.0995
t                             0.618        -1.61
D(1)                         -0.0551        0.0989
t                            -2.642         2.508
D(2)                          0.0368       -0.0533
t                             1.796        -1.377
Adjusted R-Squared            0.188         0.266
Sum Sq. Resids.               0.035         0.125
Akaike Information Criteria  -4.53         -3.257
Schwarz Criteria             -4.162        -2.889

TABLE 7 Pairwise Granger Causality Test for SAC and SAW

             Null Hypothesis
Lag (Weeks)  SAC Does Not Cause SAW  SAW Does Not Cause SAC

 1           1.386                   1.378
 2           0.891                   0.262
 3           1.889                   0.264
 4           2.748(*)                0.316
 5           2.501(*)                0.832
 6           2.099(*)                0.652
 7           1.762                   0.877
 8           1.479                   1.498
 9           1.21                    2.737(*)
10           1.0139                  2.317(*)
11           1.1896                  2.1008(*)
12           1.336                   1.872
13           1.432                   1.685
14           1.664                   1.407
15           1.717                   1.156
16           2.149(*)                1.25
17           1.897                   1.281
18           1.955                   1.188
19           1.655                   1.243
20           1.613                   1.375

Notes: Data Source: Barcelona Central Fish Market. (*) Denotes rejection
of the hypothesis of no Granger causality at 5 percent significance
level.

TABLE 8 Impulse Response to a 1 S.D. Shock for SAC and SAW

         Response of Cultured Sea Bream  Response of Wild Sea Bream
Period
(Weeks)  SAC             SAW             SAC               SAW

 1       0.021451        0               0.014035          0.038045
 2       0.014525        0.003388        0.032689          0.048494
 3       0.012753        0.004996        0.039028          0.043054
 4       0.00882         0.005289        0.035719          0.04025
 5       0.006444        0.005159        0.03197           0.041384
 6       0.004688        0.005142        0.030286          0.042488
 7       0.003854        0.005152        0.029617          0.042509
 8       0.003482        0.00513         0.029124          0.042251
 9       0.003364        0.005093        0.028779          0.042174
10       0.003343        0.005071        0.028639          0.042202
11       0.003363        0.005063        0.028626          0.042214
12       0.00339         0.00506         0.028645          0.042202
13       0.003413        0.005059        0.028661          0.042192
14       0.003427        0.005059        0.028672          0.042191
15       0.003435        0.005059        0.02868           0.042192
16       0.003439        0.005059        0.028686          0.042193
17       0.003441        0.005059        0.028689          0.042193
18       0.003441        0.005059        0.028691          0.042193
19       0.003441        0.00506         0.028691          0.042193
20       0.003441        0.00506         0.028691          0.042193

Data source: Barcelona Central Fish Market


References

Barcelona Central Fish Market (Mercabarna). Several issues. Informacio Estadistica, Barcelona.

Bene, C.; Cadren, M.; Lantz, F. "Impact of Cultured Shrimp Industry on Wild Shrimp Fisheries: Analysis of Price Determination Mechanisms and Market Dynamics," Agricultural Economics, 23, 2000, pp. 55-68.

Dickey, D.; Fuller, W. "Distribution of the Estimators for Autoregressive Time Series with a Unit Root," Journal of the American Statistical Asociation, 74, 1979, pp. 427-31.

Granger, C. "Investigating Causal Relations by Econometric Models and Cross-Spectral Methods," Econometrica, 37, 1969, pp. 424-38.

Greene, W. Econometric Analysis, Prentice Hall, 4th Edition, New Jersey, 2000.

Guttormesen, A. G. "Biological Price Generating Processes in Salmon Farming. Potential for Profitable Production Planning," in Proceedings from the 9th International Conference of the International Institute of Fisheries Economics and Trade, A. Eide and T. Vasdal (eds.), Tromso, 1998.

___. "Forecasting Weekly Salmon Prices: Risk Management in Fish Farming," Aquaculture Economics and Management, 3, 2, 1999, pp. 159-66.

Hamilton, J. Time Series Analysis, Princeton University Press, Princeton, 1994.

McKinnon, J. G. "Critical Values for Co-Integration Tests," in R. F. Engle and C. W. J. Granger (eds), Long-Run Economic Relationships, Oxford University Press, 1991, pp. 267-76.

Johansen, S. "Statistical Analysis of Cointegration Vectors," Journal of Economic Dynamics and Control, 12, 1988, pp. 231-54.

Maddala, G. S.; Kim, In-Moo. Unit Roots, Cointegration, and Structural Change, Cambridge University Press, Cambridge, 1998.

Phillips, P.; Perron, P. "Testing for a Unit Root in Time Series Regression," Biometrika, 75, 1988, pp. 335-46.

Sims, C. "Macroeconomics and Reality", Econometrica, 48, 1, pp. 1-48.

OSCAR ALFRANCA, JOAN OCA, AND LOURDES REIG*

*Universitat Politecnica de Catalunya--Spain. Comments from reviewers have been incorporated into the paper and are gratefully acknowledged. Financial support was provided by Direccio General de Recerca, Departament d'Universitats, Recerca i Societat de la Informacio project N[degrees] SGR2001-160.
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Author:Alfranca, Oscar; Oca, Joan; Reig, Lourdes
Publication:International Advances in Economic Research
Date:May 1, 2004
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