Price modelling in the Canadian fish supply chain with forecasts and simulations of the producer price of fish

ABSTRACT

This research article reports the results of two time-series models defined on the producer price of fish in Canada. An ARMAX model is specified to provide a parsimonious characterization of producer prices and used to simulate price effects from exchange rate shocks. Results show the importance of exogenous shocks, outside the control of fisheries management on welfare/income of Canadian fishermen. An error-correction model is specified to link the price in the first-hand market to the price in the processing market. This model measures both the short- and long-run parameters in defining price, provides estimates on the length of time to regain the equilibrium from price shocks and to forecast producer price response. Interestingly, results show that process price can be considered weakly exogenous with respect to both the short and long run and is the price leader in determining producer price.

KEYWORDS:

• Aggregate producer price forecasts
• ARMAX
• error-correction
• fish supply chain

Acknowledgments

The author thanks Trond Bjørndal, Audun Lem and seminar participants at FAO Price Workshop, Tokyo Japan. The comments and suggestions of the editor and two anonymous referees improved the final draft of the article.

Notes

Fishermen do have control over the quality of fish landed and the timing of harvest for farmed fish and thus some control over price.

In most markets, there will also be species and product forms that succeed in differentiating themselves from the more general market by creating a separate or segmented market (Pincinato & Asche, 2016) or by creating a margin (Caroll et al., 2002; Roheim, Gardiner, & Asche, 2007; Sogn-Grundvag, Larsen, & Young, 2014).

In recent years, there has been an increasing interest in price transmission for seafood. Some recent studies are Fernandez-Polanco & Llorente (2015), Gordon and Hussain (2015), Gordon and Maurice (2015), Singh (2016), Singh, Dey, Laowapong, & Bastola (2015), and Tveteras (2015).

There are surprisingly few studies attempting to forecast fish prices, and most focus on salmon price (Vukina & Anderson, 1993, 1994; Gu & Anderson, 1995; Guttormsen, 1999). A futures market with a price discovery role were organized for shrimp in the 1990s (Martinez-Garmendia & Anderson, 1999, 2001), but ultimately unsuccessful. During the last decade, a futures market has been operating for salmon providing price discovery and hedging services (Oglend, 2013; Asche, Oglend, & Zhang, 2014; Asche, Misund, & Oglend, 2016; Misund & Asche, 2016).

Dynamic forecasting relies on the predicted values of the ARMA components in price forecasting.

Long-run equilibrium depends on statistical cointegration amongst the price variables of interest.

Processed prices are Statistics Canada Cansim series label v1574627 and raw material prices v1576476. Statistics Canada terminated both series in 2010 and introduced a revised price index after this time. See, http://www23.statcan.gc.ca/imdb/p3VD.pl?Function=getVD&TVD=145557&CVD=145559&CPV=12111&CST=01012012&CLV=2&MLV=4 http://www.statcan.gc.ca/daily-quotidien/150528/dq150528a-eng.pdf http://www5.statcan.gc.ca/cansim/a26?lang=eng&id=3300008. Using aggregate price indices certainly blends individual fish price response but does provide an industry wide or aggregate measure of producer price response.

CPI Statistics Canada Cansim series label v41690973.

The Process index is adjusted upward by 15 points to better show individual trend.

Statistically significant at the 99% level.

Prior to November 1999 the mean of Producer price is 104.7 and 98.89 after this period. The standard error changed from 9.08 to 8.96 for the same periods, respectively. Consequently, the CV reported in Table 1 reflects both a decline in mean and standard error after November 1999.

The glsD-F has more statistical power in testing the null for near stationary variables.

We follow Gordon (1995) in setting lag length for the D-F test.

Because of what appears to be a structural break in the trend for the Producer price (Figure 1), an alternative test was carried out to check for stationary in levels with a structural break. The test is calculated at −1.07 with p-value of 0.72 and the null is again not rejected (Zivot & Andrews, 1992). There are also other examples of structural breaks in price determination processes for seafood (Asche, Oglend, & Tveteras, 2013).

This is not surprising given that most seafood prices tend to be non-stationary (Oglend & Asche, 2016).

The stationary tests are repeated using the log first-difference of each price series and in both cases the null hypothesis of non-stationary in first-differences is easily rejected.

For an interesting discussion of the first serious price forecasting model see, Gordon and Kerr (1997).

The restriction on the exogenous variables implies no feedback from the dependent variable (Enders, 2010).

Estimation is carried out using STATA 12 software.

Root mean square error and Akaike’s information criteria, respectively.

Monthly dummy variables were generated and used in estimation. Testing showed a null hypothesis of equal parameter estimates in the months of August through January could not be rejected ( with p-value = 0.8623).

In testing, the United States/Canada exchange rate is found non-stationary and first differences are used in modelling.

Using the full data set, the estimated parameters are assumed to be the true parameters in all time periods.

To be clear, with actual exchange rate at par in October 2007, we allow the exchange rate to gradually change each month until the upper bound is reached. These values are included in the dynamic forecast of Producer price. We repeat the exercise allowing the exchange rate to reach its lowest level.

The United States/Canada exchange was included in empirical work but found statistically unimportant.

An intercept could be included in Equation (4) but this would require a time trend variable in equation (3).

The half-life is a measure of the time to eliminate 50% of the deviation and is often calculated as t_half−life = ln2/γ.

The 12th lag was also necessary for specification in the ARIMA model.