1. A Short-Run Forecasting Model of the Price of Lobster
Daniel V. Gordon
Department of Economics University of Calgary
Department of Industrial Economics, University of Stavanger

2. Introduction
Economists have long been interested in forecasting the price of staple commodities
Moore's (1917) path breaking work forecasting the price and yield of cotton.
Sarle (1925) multivariate reduced form econometric modelling to forecast the price of hogs
Contributions to forecasting; agriculture, fisheries, metals, electricity using structural and reduced form models and recently univariate and multivariate time series models.

3. Objective
Reduced form econometrics forecasting Ex-vessel price of lobster, Canada
Model embedded in an error-correction framework, capture both short and long run adjustments
Measure speed of adjustment to regain the equilibrium from short-run shocks
Simulate some interesting price scenarios
Interest is policy driven; predict accurate forecasts and turning points, support planning, management and predicting income and welfare effects of fishermen

4. Why Lobster?
Collapse of the groundfish fishery, crustaceans (particularly lobster) the most important fisheries in terms of export value, in Canada
In 2008, groundfish accounted for only 9% of total value landed whereas, shellfish reached 78% of total value landed
Lobster is the premier export fishery, $680.5 million, landed volume of 75 thousand tonnes, 2013

5. Literature
Doll (1972) structural forecasting model studying a five- equation model of U.S. shrimp
Gillig et al. (1998) structural approach to measure ex-vessel price flexibilities in the Gulf of Mexico shrimp fishery
Gates and Richardson (1986) reduced form simulation model to examine prices in the American lobster fishery.
Kellog & Wang (1988) reduced form model to determine the price impact from increases in minimum size for lobster.
Greenberg et al. (1995) reduced form model to measure the price impact of increased harvest, the Alaska snow crab fishery

6. Time series techniques used in fish price forecasting.
Dupont (1993) ARIMA models to construct price forecasts that feed into a model of profit expectations on fishing location
Oglend & Sikveland (2008) use ARCH and GARCH to examine the volatility of fish prices. Variance to measure market risk.
Guttormsen (1999) price variation in farmed salmon. Classical Additive Decomposition model preformed well in predicting price but a VAR did well in predicting turning points

7. Fisheries economists serious contributions modeling the fisheries supply chain
Measure links in the supply chain at different nodes with the purpose of measuring price leadership and feedback effects
Gordon et al. 1993, Asche et al. 2004, Nielsen 2005, Asche et al. 2007, Gordon 2016, Tveteraas et al. 2016, Singh 2016
Asche et al. (2007) is a particularly interesting and important work on cross-border supply chains with tests for price leadership and exchange rate pass through

8. The current research builds on this literature
A empirical contribution in applying Pesaran’s autoregressive distributed lag/error-correction Bounds model in a fisheries context
A practical contribution in building an inverse demand forecasting model characterizing the Canadian lobster fishery
Purpose of predicting price trends and turning points

9. THE LOBSTER FISHERY
Lobster high value fishery, 78% exported to the United States
Management 45 in-shore lobster areas with some 10,000 licensed fishermen
Management input controls; limits number of traps, seasonal closures, restrictions on size and harvesting egg-bearing females
Harvest endogenous and may be correlated with error term
Test weak exogeneity, Boswijk and Urbain (1997) suggest a modified variable inclusion test

10. Real Price Canadian Lobster: monthly 1990-2015

11. Canadian and U.S. Landings Lobster

12. U.S.-Canada Exchange Rate and U.S. real GDP

13. Time Series Variables
Common observe changes in the probability structure overtime.
Non-stationary/stable variables can be spurious/misleading
Important in setting the research strategy to empirically investigate the functional relationship of interest.
Variables test ~I(1) standard cointegration and error- correction
Variables test ~I(0) and others ~I(1) standard modelling problematic.
Pesaran et al (2001) Bounds procedure valid regardless of ~I(1), ~I(0), or fractionally integrated.

14. Lag Structure
Optimal Lag Structure Under Three Alternative Summary Statistics
Variable
AIC
BIC
MAIC
Price 4 4 12
Landings Canada 4 4 12
Landings U.S. 4 4 12 Ex b 2 2 1
U.S. GDP 4 4 15
Observations
308

15. Stationary testing Variable DF glsDF PP KPSS Ex - vessel Price Level
First -
Diff
First -
Diff
First -
Diff
First -
Diff
Landings Canada
Level
Level
Level
Level
First -
Diff
First -
Diff
First -
Diff
Landings U.S.
Level
Level
Level
Level
First -
Diff
First -
Diff
Level
Exchange Rate
First -
Diff
First -
Diff
First -
Diff
First -
Diff
First -
Diff
First -
Diff
First -
Diff
U.S. GDP
First -
Diff
First -
Diff
First -
Diff
Level
First -
Diff
First -
Diff
First -
Diff

16. The Model Inverse Demand curve
𝑃 𝑡 𝑐 =𝑓( 𝐿𝑄 𝑡 𝑐 , 𝐿𝑄 𝑡 𝑢𝑠 , 𝐸𝑥 𝑡 𝑢𝑠,𝑐 , 𝐺𝐷𝑃 𝑡 𝑢𝑠 , 𝜀 𝑡 )
Combine ARDL and Error-correction
∆ 𝑃 𝑡 𝑐 = 𝛼 𝑜 + 𝑝=1 𝑃 𝛼 𝑝𝑝 ∆ 𝑃 𝑡−1 𝑐 + 𝑖=0 𝐼 𝛼 𝑐 𝑖 ∆ 𝐿𝑄 𝑡−𝑖 𝑐 + 𝑗=0 𝐽 𝛼 𝑢𝑠 𝑗 ∆ 𝐿𝑄 𝑡−𝑗 𝑢𝑠 + 𝑘=0 𝐾 𝛼 𝑒𝑥 𝑘 ∆ 𝐸𝑥 𝑡−𝑘 𝑢𝑠,𝑐 + 𝑠=0 𝑆 𝛼 𝑔𝑑𝑝 𝑠 ∆ 𝐺𝐷𝑃 𝑡−𝑠 𝑢𝑠 +
𝛾 ( 𝑃 𝑡−1 𝑐 − 𝛽 𝑜 − 𝛽 𝑐 ∙ 𝐿𝑄 𝑡−1 𝑐 − 𝛽 𝑢𝑠 ∙ 𝐿𝑄 𝑡−1 𝑢𝑠 − 𝛽 𝑒𝑥 ∙ 𝐸𝑥 𝑡−1 𝑢𝑠,𝑐 − 𝛽 𝑔𝑑𝑝 𝐺𝐷𝑃 𝑡−1 𝑢𝑠 )+ 𝜗 𝑡

17. Test weak exogeneity Possible endogeneity of Canadian landings.
Boswijk and Urbain (1997) suggest a DL model,
∆ 𝐿𝑄 𝑡 𝑐 = 𝛿 𝑜 + 𝑗=1 𝐼 𝛿 𝑗 ∆ 𝐿𝑄 𝑡−𝑖 𝑐 + 𝑖=1 𝐼 𝛿 𝑖 ∆ 𝑃 𝑡−𝑖 𝑐 +
𝑘=1 𝐾 𝛿 𝑘 ∆ 𝐿𝑄 𝑡−𝑘 𝑢𝑠 + 𝑠=1 𝑆 𝛿 𝑠 ∆ 𝐸𝑥 𝑡−𝑠 𝑢𝑠𝑐 + 𝑣=1 𝐽 𝛿 𝑗 ∆ 𝐺𝐷𝑃 𝑣−𝑗 𝑢𝑠 + 𝜖 𝑡
Long-run exogeneity can be tested by including the lagged error- correction term, 𝜀 𝑡−1 from the equilibrium (long run) as an additional regressor.
Short run exogeneity can be tested by calculating the residuals, 𝜖 𝑡 from the DL equation and used as additional variable in the error- correction

18. Distributed Lag Model Canadian Landings
Coefficient
Lag 1
Lag 2
Lag 3
Lag 4
Lag 5
Lag 6
Landings
Canadian
1.05
(0.002)a
0.938
(0.003)
-0.639
(0.000)
-0.667
-0.547
-0.189
American
7.10
1.06
(0.092)
-0.531
-0.379
0.201
(0.030)
squared
-0.114
-0.125
-0.419
-0.088
(0.033)
a Robust standard errors with p-value in parentheses.
Obs = 293, R2=0.874, BIC=445.6, p[Normality]=0.072, p[ARCH]=0.378, p[RESET]=0.347,
p[AR 1] =0.819, p[AR 2]=0.702, p[AR 3]=0.371, p[AR 4]=0.291.

19. Actual and Predicted Canadian Landings; Monthly 2014 (in-sample) - 2015 (out-of-sample).

20. Price Lobster, ARDL/EC Bounds Model
Short-run
Lag(0)
Lag(1)
Lag(2)
Lag(3)
Landings Canada
-0.099
(0.000)
0.102
0.048
0.033
(0.001)
Landings U.S.
0.035
(0.081)
-0.118
GDP U.S.
0.301
Exchange rate
-0.480
Long-run
Price
-0.419
-0.372
-0.015
(0.540)
0.718
-1.147

21. Actual and Predicted Real Lobster Price; Monthly 2014 (in-sample) - 2015 (out-of-sample).

22. Test weak exogeneity
P-value of Null hypothesis of no long-run weak exogeneity
P-value of 0.90 Null hypothesis of no short-run weak
These results support the idea that lobster fishermen maximize landings independent of current price of lobster.
Fishermen constrained by input controls and area closures, data and testing suggests that fishermen land as many lobster as possible in the time allocated

23. Long-run equilibrium
Pesaran et al (2001) and is a combination of F- and t- type procedures.
First test Null hypothesis no equilibrium, 𝐻 𝑜 : 𝛾=0 𝑎𝑛𝑑 𝛾∙𝛽=0 against the alternative of cointegration.
Second test Null hypothesis no individual link between the short- and long-run components Ho: γ=0 against the alternative Ha: γ<0.
F and t distributions are very non-standard and the contribution of Pesaran et al (2001) is in working out the distributions, which includes an inconclusive or bounds region on the range of hypothesis testing.
In testing F=24.85 and t=-9.47
Critical 5% bounds F ( ), t ( ) for k=4.

24. PRICE FORECASTING UNDER ALTERNATIVE POLICY SCENARIOS
Three alternative measures of Canadian landings:
Landings (a) three-year monthly average landings
Landings (b) is the predicted monthly landings from the estimated distributed lag model and produces an increasing monthly trend in landings.
Landings (c) is the monthly non-linear trend in the three-month average landings over the data period extended forward over the forecast period.

25. Forecast Price of Lobster, Three Canadian Landings Alternatives

26. Forecast Price of Lobster, Exchange Rate

27. Forecast Price of Lobster, Climate Change (a) $13. 15-$7. 88 (q) $14

28. Monthly High/Low Industry Revenue (millions)
High
Low
2015, actual
Revenue
$244.98
$21.29
2019, predicted
Revenue (a)*
$222.91
$19.15
Revenue (b)
$250.83
$15.86
Revenue (e)
$189.76
$15.57
Revenue (q)
$227.2
$19.34

29. Predicted Revenue: Average scenario (a) and Exchange Rate scenario (e)

31. Optimal Lag Structure Under Three Alternative Summary Statistics
Variable
AIC
BIC
MAIC
Price 4 12
Landings Canada
Landings U.S.
Exb 2 1
U.S. GDP 15
Observations
308

32. Stationary testing Variable DF glsDF PP KPSS Ex-vessel Price Level
First-Diff
Landings Canada
Landings U.S.
Exchange Rate
U.S. GDP