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Methods on Measuring
Prices Links in the Fish Supply Chain
Daniel V. Gordon
Department of Economics
University of Calgary
FAO Workshop Value Chain
Tokyo, Japan
December 2010
• 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
2
• Consider a fixed proportions relationship
between fish supply and marketing inputs
3
• Add in market Demand
4
• Assume that proportionally larger amounts of marketing
inputs are required to process increased supply of fish.
5
• 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.
6
• Substitution
7
• An interesting model by Wohlgenant (1989)
and Holloway (1991). Provides summary
measures of the price and margin flexibilities
8
1  imqimrdimmcmi LRDMCM
2  iprqiprrdiprmcpri LRDMCpr
1  ipfqipfrdipfpfi LRDMCpf
• Retail Demand Shift Variable and Marketing
Cost Index
• Consider the following price transmission
equation describing the stochastic behaviour
of fish prices.
9
• The Rd shift variable is defined as the linear
combination:
• Why is it that we require premeasured
elasticities?
• The problem is statistically consistency.
10
• The Rd index is deterministic and it might be
an advantage to introduce a stochastic error
term to account for unobserved randomness
11
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
12
13
• 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.
14
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
15
• 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
16
17
• 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.
18
• 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.
19
• ARMAX Model
• Model with stationary variables
20
tjt
q
j
jit
p
i
Vi
s
sstpot ExvesselDExExvessel   


 11
12
1
• 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
21
• 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
22
• 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
•
23
• 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
24

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Methods on measuring

  • 1. Methods on Measuring Prices Links in the Fish Supply Chain Daniel V. Gordon Department of Economics University of Calgary FAO Workshop Value Chain Tokyo, Japan December 2010
  • 2. • 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 2
  • 3. • Consider a fixed proportions relationship between fish supply and marketing inputs 3
  • 4. • Add in market Demand 4
  • 5. • Assume that proportionally larger amounts of marketing inputs are required to process increased supply of fish. 5
  • 6. • 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. 6
  • 8. • An interesting model by Wohlgenant (1989) and Holloway (1991). Provides summary measures of the price and margin flexibilities 8 1  imqimrdimmcmi LRDMCM 2  iprqiprrdiprmcpri LRDMCpr 1  ipfqipfrdipfpfi LRDMCpf
  • 9. • Retail Demand Shift Variable and Marketing Cost Index • Consider the following price transmission equation describing the stochastic behaviour of fish prices. 9
  • 10. • The Rd shift variable is defined as the linear combination: • Why is it that we require premeasured elasticities? • The problem is statistically consistency. 10
  • 11. • The Rd index is deterministic and it might be an advantage to introduce a stochastic error term to account for unobserved randomness 11
  • 12. 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 12
  • 13. 13
  • 14. • 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. 14
  • 15. 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 15
  • 16. • 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 16
  • 17. 17
  • 18. • 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. 18
  • 19. • 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. 19
  • 20. • ARMAX Model • Model with stationary variables 20 tjt q j jit p i Vi s sstpot ExvesselDExExvessel       11 12 1
  • 21. • 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 21
  • 22. • 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 22
  • 23. • 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 • 23
  • 24. • 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 24