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

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.

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

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

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

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

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

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

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

Real Price Canadian Lobster: monthly 1990-2015

Canadian and U.S. Landings Lobster

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

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.

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

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

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

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

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.

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

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

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

Test weak exogeneity P-value of 0.643 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

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 (2.86 4.01), t (-02.86 -3.99) for k=4.

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 1990-2015 extended forward over the forecast period.

Forecast Price of Lobster, Three Canadian Landings Alternatives

Forecast Price of Lobster, Exchange Rate

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

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

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

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

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