A State Space Bioeconomic Model of

Pacific Halibut

Keith R Criddle, Utah State UniversityMark Herrmann, University Alaska Fairbanks

Halibut Landings

0

25

50

75

1974 1984 1994

mill

ion

lbs

AKCAWA

IPHC regulatory areas

Approximate Structural Model with Aoki State Space Time

Series Error Correction

t t t t t t

t t t t

t

t t t t

t

t t t t t

X X X r h

r X X

z e

PDO

z z e

21 1 2 1 3 1

8 0 1 8

| 1

1| | 1

1

2

3

4

C

A B

ln ln

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Model Solution

1. GLS solution to equation 12. GLS solution to equation 2 with bias

correction3. Aoki State Space Time Series

Analysis solution to equations 3 & 4 4. Iterate steps 1, 2, and 3 until

parameter estimates converge

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Convergence of Parameter Estimates

Sto

ck D

ynam

ics

Recru

itmen

t

Coefficient on recruits

6.0

6.5

7.0

7.5

8.0

8.5

9.0

9.5

10.0

0 20 40 60 80

Coefficient on lagged biomass

1.30

1.31

1.32

1.33

1.34

1.35

1.36

0 20 40 60 80

Coefficient on lagged biomass-squared

-0.00066

-0.00064

-0.00062

-0.00060

-0.00058

-0.00056

-0.00054

-0.00052

-0.00050

0 20 40 60 80

Intercept

-3.20

-3.15

-3.10

-3.05

-3.00

-2.95

-2.90

-2.85

-2.80

0 20 40 60 80

Coefficient on biomass

-0.0040-0.0038-0.0036-0.0034-0.0032-0.0030-0.0028-0.0026-0.0024-0.0022-0.0020

0 20 40 60 80

Stock Dynamics

-100

0

100

200

300

400

500

600

1975 1980 1985 1990 1995 2000 2005

Age

8+ B

iom

ass

actualestimateresidual

( ) ( ) ( ) e-- --= - ´ + - +% % %. . . ˆ4 2

t t 1 t t 1 tt 1X 1 336 X 6 488 10 X 8 964 r h

= .2R 0 995

Recruitment Dynamics

-2

0

2

4

6

8

10

1975 1980 1985 1990 1995 2000 2005

Age

8 R

ecru

its

(mill

ion)

actualestimateresidual

( ) ( )exp exph u-- -= - - ´ +% %. . ˆ3

t t 8 t 8 t tr X 3 117 3 009 10 X

= .2R 0 519

State and Observation Equations

t

t t t t

t

t 1 t

0 3969 0 0423 0 8187

3 4244 5 2755 2 1925 z e

PDO 0 5778 0 0342 0 0984

0 3387 0 6356 0 1551

z 0 7526 0 1342 0 0334 z

0 1170 0 6265 0 2623

0

. . .

. . .

. . .

. . .

. . .

. . .

.

h

w e

+

æ ö æ ö-÷ ÷ç ç÷ ÷ç ç÷ ÷ç ç= = - - - +÷ ÷ç ç÷ ÷ç ç÷ ÷ç ç÷ ÷ç ç- -è ø è ø

æ ö- - ÷ç ÷ç ÷ç= ÷ç ÷ç ÷ç ÷ç- -è ø

-

+ t

4406 0 0356 0 4734

0 2788 0 0089 0 6137 e

0 5775 0 0227 0 3676

. .

. . .

. . .

æ ö- - ÷ç ÷ç ÷ç ÷ç ÷ç ÷ç ÷ç -è ø

Decay Path of Latent Variables

-1.5

-1

-0.5

0

0.5

1

0 2 4 6 8 10

Years

±

Eigenvalues of Moduli

0.158 0.702i 0.720

0.420 0.420

A

Gain from State Space Error Correction Procedure

R2

w/o Correction w/ Correction

Stock Dynamics Equation

0.994 0.995

Recruitment Dynamics Equation

0.087(0.682 in ln)

0.519

Expected Sustainable Yields

0

25

50

75

100

125

0 250 500 750Age 8+ Biomass (million lbs)

Sust

ainab

le Y

ield

(m

illio

n lb

s)

Expected Recruitment

0

2

4

6

8

0 250 500 750Age 8+ Biomass (million lbs)

Age

8 R

ecru

its

(mill

ion)

Sustainable Yield and Recruitment: ± 10% Change in Productivity

0

25

50

75

100

125

0 250 500 750Age 8+ Biomass (million lbs)

Sust

ainab

le Y

ield

(m

illio

n lb

s)

0

2

4

6

8

0 250 500 750Age 8+ Biomass (million lbs)

Age 8

Recru

its

(mill

ions)

Sustainable Yield and Recruitment: ± 10% Change in Recruitment

0

25

50

75

100

125

0 250 500 750Age 8+Biomass (million lbs)

Sust

ainab

le Y

ield

(m

illio

n lb

s)

0

2

4

6

8

0 250 500 750Age 8+ Biomass (million lbs)

Age 8

Recru

its

(mill

ions)

Sustainable Yield and Recruitment:

± 5% Change in Growth Rate

0

25

50

75

100

125

0 250 500 750Age 8+ Biomass (million lbs)

Sust

ainab

le Y

ield

(m

illio

n lb

s)

0

2

4

6

8

0 250 500 750Age 8+ Biomass (million lbs)

Age 8

Recru

its

(mill

ions)

Product and Financial Flows in the Halibut

Market

British Columbia halibut capture fishery

U.S. (Alaska and Washington) Pacific halibut capture fishery

U.S. market

U.S. inventories U.S. processing Canadian processing

Other minor markets

Other minor supplies

Market Model

US Wholesale Demand R2 = 0.871US Inventories R2 = 0.446BC Exports R2 = 0.795BC Export Price R2 = 0.946AK Exvessel Demand R2 = 0.899BC Exvessel Demand R2 = 0.882

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Economic Effects of

IFQs

Wholesale price ($/lb)

AK exvessel

price ($/lb)

Exvessel Revenue ($million)

BC exvessel

price ($/lb)

w/o IFQ 2.50 1.80 90.8 2.45

w/ IFQ 2.74 2.02 101.7 2.13

% Change + 8.7% + 10.7% + 10.7% - 15.1%

Expected Effects of Season Elongation

Wholesale price ($/lb)

Exvessel price ($/lb)

Exvessel Revenue ($million)

245 Day Season

2.90 2.21 128.5

321 Day Season

2.95 2.25 130.8

% Change + 1.6% + 1.8% + 1.8%

365 Day Season

3.02 2.32 134.7

% Change + 4.1% + 4.9% + 4.9%

Expected Effects of Increased Aquaculture

Aquaculture (million lbs)

Wholesale price ($/lb)

Exvessel price ($/lb)

Exvessel Revenue ($million)

0 3.02 2.32 134.5

14.5 2.66 1.99 115.7

29.1 2.30 1.66 96.4

43.6 1.95 1.33 77.3

58.1 1.59 1.00 58.2

Sustainable Exvessel Revenues: ± 10% Change in

Productivity

0

25

50

75

100

125

150

175

0 250 500 750Age 8+ Biomass (million lbs)

$ m

illio

n

Sustainable Exvessel Revenues: ± 10% Change in

Productivity

0

25

50

75

100

125

150

175

0 25 50 75 100 125 150Coastwide Landings (million lbs)

$ m

illio

n

MSY

Sustainable Exvessel Revenues: ± 10% Change in

Recruitment

0

25

50

75

100

125

150

175

0 250 500 750Age 8+ Biomass (million lbs)

$ m

illio

n

Sustainable Exvessel Revenues: ± 10% Change in

Recruitment

0

25

50

75

100

125

150

175

0 25 50 75 100 125 150Coastwide Landings (million lbs)

$ m

illio

n

MSY

Sustainable Exvessel Revenues: ± 5% Change in

Growth Rate

0

25

50

75

100

125

150

175

0 250 500 750Age 8+ Biomass (million lbs)

$ m

illio

n

Sustainable Exvessel Revenues: ± 5% Change in

Growth Rate

0

25

50

75

100

125

150

175

0 25 50 75 100 125 150Coastwide Landings (million lbs)

$ m

illio

n

MSY

What Next?

• Age/Sex structure to stock and recruitment dynamics

• Spatial structure to stock and recruitment dynamics

• Use ENSO instead of PDO to gain from lag• Include model production costs

• Stochastic Optimal Control of catches and inventories

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The End