Methods on MeasuringPrices Links in the Fish Supply Chain

Daniel V. GordonDepartment of Economics

University of Calgary

FAO Workshop Value ChainTokyo, Japan

December 2010

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• Introduction• The demand for fish is derived by end-use

demand for the commodity. • The retail price will reflect the fish price plus the

cost of marketing the commodity from the vessel to the retail level.

• Let the retail/vessel price margin be the difference between the retail and vessel price.

• The impact of a shock somewhere in the supply chain on price will depend on the structure of the relationship between the two sectors

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• Consider a fixed proportions relationship between fish supply and marketing inputs

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• Add in market Demand

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• Assume that proportionally larger amounts of marketing inputs are required to process increased supply of fish.

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• Supply of marketing inputs is perfectly elastic but substitution possibilities exist between the fish commodity and marketing inputs, the derived fish demand curve is more elastic

• Wohlgenant and Haidacher (1989) argue that processors can choose alternative production processes, including different modes of transporting, interproduct substitutability and the substitution of quality for quantity.

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• Substitution

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• An interesting model by Wohlgenant (1989) and Holloway (1991). Provides summary measures of the price and margin flexibilities

1 imqimrdimmcmi LRDMCM

2 iprqiprrdiprmcpri LRDMCpr

1 ipfqipfrdipfpfi LRDMCpf

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• Retail Demand Shift Variable and Marketing Cost Index

• Consider the following price transmission equation describing the stochastic behaviour of fish prices.

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• The Rd shift variable is defined as the linear combination:

• Why is it that we require premeasured elasticities?

• The problem is statistically consistency.

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• The Rd index is deterministic and it might be an advantage to introduce a stochastic error term to account for unobserved randomness

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Estimated Elasticities

Price of Sirloin/kg

Price of chicken/kg

Price of Non-Food

Income Population

Estimated Elasticity

0.25 0.15 0.09 0.81 1.0

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• Marketing Cost Index• The Mc index is a weighted price index of the

cost of inputs used in moving fish product through the supply chain. We have identified four major inputs in fish processing; labour, electricity, transportation and packaging. The weights in the index reflect the cost share of the input in the total cost of processing.

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Cost Share Major Inputs Fish Processing

Price of Labour

Price of Electricity

Price of Transportation

Price of Packaging

Cost Share 0.51 0.18 0.16 0.15

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• Mc index is written

• Combining the real price indices with the cost shares we are able to predict the marketing cost index for seafood processing

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• Reduced Form Models • This price approach is based on the theory of

derived demand where the processed price of fish is used as a proxy for market factors setting the ex-vessel price.

• Univariate analysis is carried out on the ex-vessel price of fish.

• The ARMAX model is well identified and will allow for dynamic forecasts of ex-vessel prices.

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• Selecting the correct lag specification critical for generating an estimated equation with good forecasting potential.

• Review the autocorrelation and partial autocorrelation functions

• Candidate specifications defined on testing iid • Box-Lung Q-statistic RMSE and AIC statistics.

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• ARMAX Model

• Model with stationary variables

tjt

q

jjit

p

iVi

ssstpot ExvesselDExExvessel

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1

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• Error-Correction Modelling • Recognizing the structural links between the

first-hand and processing, we postulate a long-run price relationship.

• An error-correction (EC) model can be used to econometrically identify both the short- and long- run parameters for the first-hand market and predict the length of time for price adjustment to regain the long-run equilibrium

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• In a pairwise comparison of prices it is not unreasonable to think of an economic equilibrium describing the long-run relationship and written in basic form as

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• in a short run distributed lag representation the error-correction model can be written

• All arguments stationary • The speed of adjustment to a short-run price

shock can be approximated •

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• Testing weak exogeneity

• Long-run exogeneity tested by including the error-correction term as an additional regressor.

• Short-run exogeneity tested by using fitted residuals from this equation and adding this as an additional variable error correction