a state space bioeconomic model of pacific halibut keith r criddle, utah state university mark...
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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
Microsoft Word Document
Microsoft Word Document
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
Microsoft Word Document
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
Microsoft Word Document
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
Microsoft Word Document
The End
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